Edit Profile (opens in new tab) Böttcher, Albrecht Co-Author Distance Author ID: bottcher.albrecht Published as: Böttcher, Albrecht; Böttcher, A.; Boettcher, A.; Boettcher, Albrecht more...less Homepage: https://www-user.tu-chemnitz.de/~aboettch/ External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef Documents Indexed: 235 Publications since 1980, including 9 Books and 4 Additional arXiv Preprints 11 Contributions as Editor · 1 Further Contribution Reviewing Activity: 8 Reviews Biographic References: 8 Publications Co-Authors: 96 Co-Authors with 201 Joint Publications 3,350 Co-Co-Authors all top 5 Co-Authors 46 single-authored 54 Grudsky, Sergei Mikhailovich 34 Silbermann, Bernd 28 Spitkovsky, Ilya Matvey 19 Karlovich, Yuri I. 14 Maksimenko, Egor A. 9 Bogoya, Johan M. 9 Fukshansky, Lenny 8 Garcia, Stephan Ramon 8 Widom, Harold 7 Wolf, Hartmut 6 Gohberg, Israel 6 Heidler, Harald 6 Kaashoek, Marinus Adriaan 6 Maharaj, Hiren 6 Wenzel, David 5 Basor, Estelle L. 5 Dörfler, Peter 5 Ehrhardt, Torsten 5 Embree, Mark 4 Iserles, Arieh 4 Kozak, Anatoli V. 4 Potts, Daniel 4 Rabinovich, Vladimir Samuilovich 4 Roch, Steffen 3 Brualdi, Richard Anthony 3 Dym, Harry 3 Ramírez de Arellano, Enrique 3 Ran, André C. M. 3 Sokolov, Viatcheslav I. 3 Speck, Frank-Olme 3 Tracy, Craig Arnold 2 Bini, Dario Andrea 2 Bogoya, Manuel 2 Crespo, Pedro M. 2 dos Santos, António Ferreira 2 Gutiérrez-Gutiérrez, Jesús 2 Halwass, Martin 2 Karlovych, Oleksiy 2 Krupnik, Naum Yakovlevich 2 Simon, Barry 2 Unterberger, Jérémie M. 1 Al-Musallam, Fadhel A. 1 Barrera, Mauricio 1 Bishop, Christopher James 1 Brunner, Hermann 1 Butzer, Paul Leo 1 Chithra, A. V. 1 Corwin, Ivan Z. 1 Diaconis, Persi Warren 1 Dijksma, Aad 1 Dritschel, Michael A. 1 Dzhirgalova, Svetlana 1 Eisenbarth, Simon 1 Feistauer, Miloslav 1 Garoni, Carlo 1 Gasca, Juanita 1 Gemignani, Luca 1 Heinig, Georg 1 Hofmann, Bernd 1 Hogben, Leslie 1 Hurák, Zdeněk 1 Hurd, Robert Allan 1 Huybrechs, Daan 1 Jones, Douglas Samuel 1 Junghanns, Peter 1 Kelley, Al 1 Kittaneh, Fuad 1 Kozel, Karel 1 Kunis, Stefan 1 Langenau, Holger 1 Langer, Heinz 1 Latz, Norbert 1 Lebre, Amarino Brites 1 Leis, Rolf 1 Lindner, Marko 1 Maz’ya, Vladimir Gilelevich 1 Meister, Claudia-Veronika 1 Meister, Ljudmila 1 Meister, Olaf 1 Mitkovski, Mishko 1 Namboodiri, M. N. N. 1 Nazarov, SergueíA. 1 Needell, Deanna 1 Neustupa, Jiří 1 Nørsett, Syvert Paul 1 Omar, Mohamed 1 O’Neill, Christopher 1 Otte, Peter 1 Pack, Donald Cecil 1 Perälä, Antti Ilmari 1 Pietsch, Albrecht 1 Polettini, Matteo 1 Pontecorvo, Largo Bruno 1 Rebs, Christian 1 Rost, Karla 1 Rovnyak, James 1 Schwartz, Moshe 1 Šebek, Michael 1 Serra-Capizzano, Stefano 1 Seybold, Martin P. ...and 12 more Co-Authors all top 5 Serials 26 Linear Algebra and its Applications 20 Integral Equations and Operator Theory 12 Mathematische Nachrichten 6 Operator Theory: Advances and Applications 5 Journal of Functional Analysis 5 Zeitschrift für Analysis und ihre Anwendungen 5 ELA. The Electronic Journal of Linear Algebra 4 Journal of Integral Equations and Applications 3 Journal of Mathematical Analysis and Applications 3 Wissenschaftliche Zeitschrift der Technischen Hochschule Karl-Marx-Stadt 3 Acta Scientiarum Mathematicarum 3 Archiv der Mathematik 3 Journal of Computational and Applied Mathematics 3 SIAM Journal on Matrix Analysis and Applications 3 Doklady Mathematics 3 Operators and Matrices 2 Journal of Approximation Theory 2 Monatshefte für Mathematik 2 SIAM Journal on Numerical Analysis 2 Soviet Mathematics. Doklady 2 Journal of Operator Theory 2 Revista Matemática Iberoamericana 2 Asymptotic Analysis 2 Bulletin of the American Mathematical Society. New Series 2 St. Petersburg Mathematical Journal 2 ETNA. Electronic Transactions on Numerical Analysis 2 The New York Journal of Mathematics 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Sbornik: Mathematics 2 Journal of Spectral Theory 1 Applicable Analysis 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Statistical Physics 1 Mathematical Methods in the Applied Sciences 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Rocky Mountain Journal of Mathematics 1 Studia Mathematica 1 Mathematics of Computation 1 Wissenschaftliche Zeitschrift der Technischen Universität Chemnitz 1 Bulletin of the London Mathematical Society 1 Calcolo 1 Functional Analysis and its Applications 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Algebra 1 Journal of the London Mathematical Society. Second Series 1 Journal of Number Theory 1 Journal of Soviet Mathematics 1 Manuscripta Mathematica 1 Mathematica Scandinavica 1 Numerical Functional Analysis and Optimization 1 SIAM Journal on Control and Optimization 1 Transactions of the American Mathematical Society 1 Soviet Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 Acta Applicandae Mathematicae 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Discrete & Computational Geometry 1 SIAM Journal on Discrete Mathematics 1 Algebra i Analiz 1 Numerical Algorithms 1 Aequationes Mathematicae 1 SIAM Journal on Mathematical Analysis 1 Notices of the American Mathematical Society 1 Irish Mathematical Society Bulletin 1 Indagationes Mathematicae. New Series 1 Journal of Mathematical Sciences (New York) 1 Numerical Linear Algebra with Applications 1 Methods and Applications of Analysis 1 Integral Transforms and Special Functions 1 Electronic Journal of Probability 1 The Journal of Fourier Analysis and Applications 1 Documenta Mathematica 1 Methods of Functional Analysis and Topology 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Computational Methods and Function Theory 1 Fields Institute Monographs 1 Progress in Mathematics 1 Texts and Readings in Mathematics 1 Communications in Mathematical Analysis 1 Complex Analysis and Operator Theory 1 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 1 Research in Number Theory 1 Universitext 1 Springer Monographs in Mathematics 1 Mathematical Research all top 5 Fields 190 Operator theory (47-XX) 110 Linear and multilinear algebra; matrix theory (15-XX) 49 Integral equations (45-XX) 49 Numerical analysis (65-XX) 36 Functional analysis (46-XX) 24 Harmonic analysis on Euclidean spaces (42-XX) 19 Functions of a complex variable (30-XX) 14 History and biography (01-XX) 13 Approximations and expansions (41-XX) 11 Number theory (11-XX) 9 General and overarching topics; collections (00-XX) 9 Combinatorics (05-XX) 9 Real functions (26-XX) 9 Probability theory and stochastic processes (60-XX) 7 Difference and functional equations (39-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 Associative rings and algebras (16-XX) 5 Convex and discrete geometry (52-XX) 4 Information and communication theory, circuits (94-XX) 3 Field theory and polynomials (12-XX) 3 Ordinary differential equations (34-XX) 2 Commutative algebra (13-XX) 2 Group theory and generalizations (20-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Partial differential equations (35-XX) 2 Abstract harmonic analysis (43-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Optics, electromagnetic theory (78-XX) 2 Systems theory; control (93-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Sequences, series, summability (40-XX) 1 General topology (54-XX) 1 Statistics (62-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 197 Publications have been cited 2,749 times in 1,512 Documents Cited by ▼ Year ▼ Introduction to large truncated Toeplitz matrices. Zbl 0916.15012 Böttcher, Albrecht; Silbermann, Bernd 309 1999 Analysis of Toeplitz operators. Prepared jointly with Alexei Karlovich. 2nd ed. Zbl 1098.47002 Böttcher, Albrecht; Silbermann, Bernd 275 2006 Spectral properties of banded Toeplitz matrices. Zbl 1089.47001 Böttcher, Albrecht; Grudsky, Sergei M. 192 2005 Analysis of Toeplitz operators. Lizenzausg. d. Akademie-Verl. Berlin. Zbl 0732.47029 Böttcher, Albrecht; Silbermann, Bernd 125 1990 Carleson curves, Muckenhoupt weights, and Toeplitz operators. Zbl 0889.47001 Böttcher, Albrecht; Karlovich, Yuri I. 115 1997 A gentle guide to the basics of two projections theory. Zbl 1189.47073 Böttcher, A.; Spitkovsky, I. M. 105 2010 Convolution operators and factorization of almost periodic matrix functions. Zbl 1011.47001 Böttcher, Albrecht; Karlovich, Yu I.; Spitkovsky, I. M. 97 2002 The Frobenius norm and the commutator. Zbl 1173.15010 Böttcher, Albrecht; Wenzel, David 43 2008 Pseudospectra and singular values of large convolution operators. Zbl 0819.45002 Böttcher, Albrecht 42 1994 Toeplitz matrices, asymptotic linear algebra, and functional analysis. Zbl 0969.47022 Böttcher, Albrecht; Grudsky, S. M. 42 2000 How big can the commutator of two matrices be and how big is it typically? Zbl 1077.15020 Böttcher, Albrecht; Wenzel, David 41 2005 Invertibility and asymptotics of Toeplitz matrices. Zbl 0578.47015 Böttcher, Albrecht; Silbermann, Bernd 39 1983 Toeplitz operators with piecewise quasisectorial symbols. Zbl 0721.47028 Böttcher, A.; Silbermann, B.; Spitkovskij, I. M. 38 1990 On the condition numbers of large semi-definite Toeplitz matrices. Zbl 0934.15005 Böttcher, Albrecht; Grudsky, Sergei M. 36 1998 Toeplitz matrices and determinants with Fisher-Hartwig symbols. Zbl 0592.47016 Böttcher, Albrecht; Silbermann, Bernd 31 1985 Eigenvalues of Hermitian Toeplitz matrices with smooth simple-loop symbols. Zbl 1302.65086 Bogoya, J. M.; Böttcher, A.; Grudsky, S. M.; Maximenko, E. A. 30 2015 Inside the eigenvalues of certain Hermitian Toeplitz band matrices. Zbl 1195.15009 Böttcher, A.; Grudsky, S. M.; Maksimenko, E. A. 30 2010 The method of limit operators for one-dimensional singular integrals with slowly oscillating data. Zbl 0993.47026 Böttcher, A.; Karlovich, Yu. I.; Rabinovich, V. S. 30 2000 Convergence rates for Tikhonov regularization from different kinds of smoothness conditions. Zbl 1110.65041 Böttcher, Albrecht; Hofmann, Bernd; Tautenhahn, Ulrich; Yamamoto, Masahiro 25 2006 Toeplitz operators and determinants generated by symbols with one Fisher- Hartwig singularity. Zbl 0613.47024 Böttcher, Albrecht; Silbermann, Bernd 24 1986 Banach algebras generated by \(N\) idempotents and applications. Zbl 0885.46041 Böttcher, A.; Gohberg, I.; Karlovich, Yu.; Krupnik, N.; Roch, S.; Silbermann, B.; Spitkovsky, I. 23 1996 Norms of inverses, spectra, and pseudospectra of large truncated Wiener-Hopf operators and Toeplitz matrices. Zbl 0887.47025 Boettcher, A.; Grudsky, S. M.; Silbermann, B. 23 1997 From Toeplitz eigenvalues through Green’s kernels to higher-order Wirtinger-Sobolev inequalities. Zbl 1118.47016 Böttcher, Albrecht; Widom, Harold 22 2006 Structured condition numbers of large Toeplitz matrices are rarely better than usual condition numbers. Zbl 1164.15309 Böttcher, A.; Grudsky, S. M. 22 2005 The finite section method for Toeplitz operators on the quarter-plane with piecewise continuous symbols. Zbl 0549.47010 Böttcher, Albrecht; Silbermann, Bernd 19 1983 Szegő via Jacobi. Zbl 1116.47024 Böttcher, Albrecht; Widom, Harold 18 2006 Eigenvectors of Hermitian Toeplitz matrices with smooth simple-loop symbols. Zbl 1331.47046 Bogoya, J. M.; Böttcher, A.; Grudsky, S. M.; Maximenko, E. A. 17 2016 Infinite matrices and projection methods. Zbl 0842.65032 Böttcher, Albrecht 16 1996 A general look at local principles with special emphasis on the norm computation aspect. Zbl 0655.46036 Böttcher, A.; Krupnik, N.; Silbermann, B. 16 1988 Pseudodifferential operators with heavy spectrum. Zbl 0810.47048 Böttcher, A.; Spitkovsky, I. M. 15 1994 Approximation of approximation numbers by truncation. Zbl 1021.47009 Böttcher, A.; Chithra, A. V.; Namboodiri, M. N. N. 15 2001 Wiener-Hopf integral operators with \(PC\) symbols on spaces with Muckenhoupt weight. Zbl 0779.45002 Böttcher, Albrecht; Spitkovsky, Ilya M. 15 1993 Exploration of Toeplitz-like matrices with unbounded symbols is not a purely academic journey. Zbl 1482.47049 Böttcher, Albrecht; Garoni, Carlo; Serra-Capizzano, Stefano 15 2017 The asymptotic behavior of Toeplitz determinants for generating functions with zeros of integral orders. Zbl 0479.47025 Boettcher, Albrecht; Silbermann, Bernd 14 1981 Weighted Markov-type inequalities, norms of Volterra operators, and zeros of Bessel functions. Zbl 1186.41004 Böttcher, Albrecht; Dörfler, Peter 14 2010 Two elementary derivations of the pure Fisher–Hartwig determinant. Zbl 1081.47033 Böttcher, Albrecht; Widom, Harold 14 2005 Functions of banded Hermitian block Toeplitz matrices in signal processing. Zbl 1115.47059 Gutiérrez-Gutiérrez, Jesús; Crespo, Pedro M.; Böttcher, Albrecht 13 2007 A Gohberg-Kurpnik-Sarason symbol calculus for algebras of Toeplitz, Hankel, Cauchy and Carleman operators. Zbl 0727.47037 Böttcher, A.; Roch, S.; Silbermann, B.; Spitkovskii, I. M. 13 1990 Asymptotics of Toeplitz and Wiener-Hopf operators. Zbl 0689.45009 Böttcher, Albrecht; Silbermann, Bernd 13 1989 On the determinant formulas by Borodin, Okounkov, Baik, Deift and Rains. Zbl 1040.47016 Böttcher, Albrecht 12 2002 Mellin pseudodifferential operators with slowly varying symbols and singular integrals on Carleson curves with Muckenhoupt weights. Zbl 0913.47046 Böttcher, A.; Karlovich, Yu. I.; Rabinovich, V. S. 12 1998 One more proof of the Borodin-Okounkov formula for Toeplitz determinants. Zbl 0992.47013 Böttcher, A. 12 2001 Discrete Wiener-Hopf operators on spaces with Muckenhoupt weight. Zbl 0971.47021 Böttcher, A. 12 2000 Maximum norm versions of the Szegő and Avram-Parter theorems for Toeplitz matrices. Zbl 1320.15028 Bogoya, J. M.; Böttcher, A.; Grudsky, S. M.; Maximenko, E. A. 12 2015 On the best constants in inequalities of the Markov and Wirtinger types for polynomials on the half-line. Zbl 1162.41004 Böttcher, Albrecht; Dörfler, Peter 12 2009 Toeplitz operators with symbols from \(C+H^{\infty}\) in the space \(\ell ^ p\). Zbl 0666.47016 Böttcher, A.; Silbermann, B. 12 1989 On the singular values and eigenvalues of the Fox-Li and related operators. Zbl 1233.47022 Böttcher, Albrecht; Brunner, Hermann; Iserles, Arieh; Nørsett, Syvert P. 11 2010 Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices. Zbl 1388.15028 Böttcher, Albrecht; Bogoya, Johan M.; Grudsky, Sergei M.; Maximenko, Egor A. 11 2017 Similarity between two projections. Zbl 1508.47021 Böttcher, Albrecht; Simon, Barry; Spitkovsky, Ilya 11 2017 Notes on the asymptotic behavior of block Toeplitz matrices and determinants. Zbl 0468.47016 Böttcher, Albrecht; Silbermann, Bernd 10 1980 The constants in the asymptotic formulas by Rambour and Seghier for inverses of Toeplitz matrices. Zbl 1070.47015 Böttcher, A. 10 2004 Asymptotics of individual eigenvalues of a class of large Hessenberg Toeplitz matrices. Zbl 1390.15094 Bogoya, J. M.; Böttcher, A.; Grudsky, S. M. 10 2012 A Newton method for canonical Wiener-Hopf and spectral factorization of matrix polynomials. Zbl 1303.47026 Böttcher, Albrecht; Halwass, Martin 10 2013 Drazin inversion in the von Neumann algebra generated by two orthogonal projections. Zbl 1178.47026 Böttcher, A.; Spitkovsky, I. M. 10 2009 The spectra of large Toeplitz band matrices with a randomly perturbed entry. Zbl 1022.47019 Böttcher, A.; Embree, M.; Sokolov, V. I. 9 2003 \(C^*\)-algebras in numerical analysis. Zbl 1061.46050 Böttcher, Albrecht 9 2000 The \(C^{*}\)-algebra of singular integral operators with semi-almost periodic coefficients. Zbl 1048.47027 Böttcher, A.; Karlovich, Yu. I.; Spitkovsky, I. M. 9 2003 The Onsager formula, the Fisher-Hartwig conjecture, and their influence on research into Toeplitz operators. Zbl 1080.47502 Böttcher, Albrecht 9 1995 Toeplitz operators with PQS symbols on weighted Hardy spaces. Zbl 0735.47013 Böttcher, Albrecht; Spitkovksy, Ilya M. 9 1991 Wiener-Hopf determinants with rational symbols. Zbl 0691.45004 Böttcher, Albrecht 9 1989 Singular integral operators with complex conjugation from the viewpoint of pseudodifferential operators. Zbl 1004.45010 Böttcher, A.; Karlovich, Yu. I.; Rabinovich, V. S. 9 2001 On certain finite-dimensional algebras generated by two idempotents. Zbl 1235.15017 Böttcher, A.; Spitkovsky, I. M. 9 2011 Spectral theory of large Wiener-Hopf operators with complex-symmetric kernels and rational symbols. Zbl 1227.47015 Böttcher, Albrecht; Grudsky, Sergei; Iserles, Arieh 9 2011 Singular integral equations with PQC coefficients and freely transformed argument. Zbl 0832.45001 Böttcher, A.; Karlovich, Yu. I.; Silbermann, B. 8 1994 Toeplitz matrices, asymptotic linear algebra and functional analysis. Zbl 0952.47025 Böttcher, Albrecht; Grudsky, S. M. 8 2000 On the corona theorem for almost periodic functions. Zbl 0931.46036 Böttcher, A. 8 1999 Toeplitz operators with frequency modulated semi-almost periodic symbols. Zbl 0996.47035 Böttcher, A.; Grudsky, S.; Spitkovsky, I. 8 2001 Toeplitz operators with discontinuous symbols: Phenomena beyond piecewise continuity. Zbl 0887.47026 Böttcher, A.; Grudsky, S. M. 8 1996 Toeplitz operators with PC symbols on general Carleson Jordan curves with arbitrary Muckenhoupt weights. Zbl 0918.47025 Böttcher, Albrecht; Karlovich, Yuri I. 8 1999 Toeplitz determinants with perturbations in the corners. Zbl 1300.15010 Böttcher, Albrecht; Fukshansky, Lenny; Garcia, Stephan Ramon; Maharaj, Hiren 8 2015 From convergence in distribution to uniform convergence. Zbl 1419.60005 Bogoya, J. M.; Böttcher, A.; Maximenko, E. A. 8 2016 Eigenvalues of Hermitian Toeplitz matrices with polynomially increasing entries. Zbl 1258.15011 Bogoya, Johan M.; Böttcher, Albrecht; Grudsky, Sergei M. 8 2012 Eigenvalue clusters of large tetradiagonal Toeplitz matrices. Zbl 1477.47023 Böttcher, Albrecht; Gasca, Juanita; Grudsky, Sergei M.; Kozak, Anatoli V. 8 2021 Wiener-Hopf and spectral factorization of real polynomials by Newton’s method. Zbl 1281.65075 Böttcher, Albrecht; Halwass, Martin 8 2013 Spectral approximation of banded Laurent matrices with localized random perturbations. Zbl 0995.47021 Böttcher, Albrecht; Embree, Mark; Lindner, Marko 8 2002 Toeplitz and singular integral operators on Carleson curves with logarithmic whirl points. Zbl 0823.47027 Böttcher, Albrecht; Karlovich, Yuri I. 7 1995 On large Toeplitz band matrices with an uncertain block. Zbl 1021.15008 Böttcher, A.; Embree, M.; Sokolov, V. I. 7 2003 Norms of Toeplitz matrices with Fisher–Hartwig symbols. Zbl 1145.47023 Böttcher, Albrecht; Virtanen, Jani 7 2007 Mass concentration in quasicommutators of Toeplitz matrices. Zbl 1128.47063 Böttcher, Albrecht; Gutiérrez-Gutiérrez, Jesús; Crespo, Pedro M. 7 2007 The spectrum is discontinuous on the manifold of Toeplitz operators. Zbl 0966.47015 Böttcher, A.; Grudsky, S.; Spitkovsky, I. 7 2000 Harold Widom’s work in Toeplitz operators. Zbl 07501948 Basor, Estelle; Böttcher, Albrecht; Ehrhardt, Torsten 7 2022 A continuous analogue of the Fisher-Hartwig formula for piecewise continuous symbols. Zbl 0822.47026 Böttcher, A.; Silbermann, B.; Widom, H. 7 1994 Orthogonal and skew-symmetric operators in real Hilbert space. Zbl 1277.47022 Böttcher, Albrecht; Pietsch, Albrecht 7 2012 The factorization problem: some known results and open questions. Zbl 1280.47027 Böttcher, Albrecht; Spitkovsky, Ilya M. 7 2013 Discrete one-dimensional zero-order pseudodifferential operators on spaces with Muckenhoupt weight. Zbl 1035.47025 Böttcher, A.; Seybold, M. 7 2002 Infinite Toeplitz and Laurent matrices with localized impurities. Zbl 0995.15013 Böttcher, A.; Embree, M.; Sokolov, V. I. 7 2002 Probability against condition number and sampling of multivariate trigonometric random polynomials. Zbl 1171.65389 Böttcher, Albrecht; Potts, Daniel 7 2007 On the eigenvalues of certain canonical higher-order ordinary differential operators. Zbl 1110.34060 Böttcher, Albrecht; Widom, Harold 6 2006 Emergence, persistence, and disappearance of logarithmic spirals in the spectra of singular integral operators. Zbl 0865.45003 Böttcher, A.; Karlovich, Yu. I.; Rabinovich, V. S. 6 1996 On lattices generated by finite abelian groups. Zbl 1328.11077 Böttcher, Albrecht; Fukshansky, Lenny; Garcia, Stephan Ramon; Maharaj, Hiren 6 2015 Classification of the finite-dimensional algebras generated by two tightly coupled idempotents. Zbl 1285.16020 Böttcher, A.; Spitkovsky, I. M. 6 2013 Eigenvectors of Hessenberg Toeplitz matrices and a problem by Dai, Geary, and Kadanoff. Zbl 1260.15009 Bogoya, J. M.; Böttcher, A.; Grudsky, S. M.; Maksimenko, E. A. 6 2012 On the structure of the eigenvectors of large Hermitian Toeplitz band matrices. Zbl 1267.47044 Böttcher, Albrecht; Grudsky, Sergei M.; Maksimenko, Egor A. 6 2010 The first order asymptotics of the extreme eigenvectors of certain Hermitian Toeplitz matrices. Zbl 1181.47023 Böttcher, A.; Grudsky, S.; Maksimenko, E. A.; Unterberger, J. 6 2009 Toeplitz determinants with piecewise continuous generating function. Zbl 0519.47015 Boettcher, A. 6 1982 Block Toeplitz operators with frequency-modulated semi-almost periodic symbols. Zbl 1036.47014 Böttcher, A.; Grudsky, S.; Spitkovsky, I. 5 2003 Asymptotic spectra of dense Toeplitz matrices are unstable. Zbl 1038.65030 Böttcher, A.; Grudsky, S. M. 5 2003 The norm of the product of a large matrix and a random vector. Zbl 1065.15032 Böttcher, Albrecht; Grudsky, Sergei 5 2003 Piecewise continuous Toeplitz matrices and operators: Slow approach to infinity. Zbl 1022.47018 Böttcher, Albrecht; Embree, Mark; Trefethen, Lloyd N. 5 2002 Pushing the envelope of the test functions in the Szegö and Avram-Parter theorems. Zbl 1153.15012 Böttcher, Albrecht; Grudsky, Sergei M.; Maksimenko, Egor A. 5 2008 Asymptotic eigenvalue expansions for Toeplitz matrices with certain Fisher-Hartwig symbols. Zbl 07798264 Bogoya, M.; Böttcher, A.; Grudsky, S. M. 3 2023 Core invertibility of operators from the algebra generated by two orthogonal projections. Zbl 1549.47081 Böttcher, Albrecht; Spitkovsky, Ilya M. 1 2023 Harold Widom’s work in Toeplitz operators. Zbl 07501948 Basor, Estelle; Böttcher, Albrecht; Ehrhardt, Torsten 7 2022 Remembrances of Harold Widom. Zbl 1493.01041 Basor, Estelle; Böttcher, Albrecht; Corwin, Ivan; Diaconis, Persi; Ehrhardt, Torsten; Kelley, Al; Simon, Barry; Tracy, Craig A.; Tromba, Tony 3 2022 Toeplitz operators and random matrices. In memory of Harold Widom. Zbl 1519.47002 2 2022 My encounters with Harold Widom. Zbl 1535.01055 Böttcher, Albrecht 2 2022 Harold Widom’s contributions to the spectral theory and asymptotics of Toeplitz operators and matrices. Zbl 07827897 Basor, Estelle; Böttcher, Albrecht; Ehrhardt, Torsten 1 2022 Eigenvalue clusters of large tetradiagonal Toeplitz matrices. Zbl 1477.47023 Böttcher, Albrecht; Gasca, Juanita; Grudsky, Sergei M.; Kozak, Anatoli V. 8 2021 Weighted means of B-splines, positivity of divided differences, and complete homogeneous symmetric polynomials. Zbl 1458.05253 Böttcher, Albrecht; Garcia, Stephan Ramon; Omar, Mohamed; O’Neill, Christopher 3 2021 The norm attainment problem for functions of projections. Zbl 07394760 Böttcher, Albrecht; Spitkovsky, Ilya M. 2 2021 Representing integers by multilinear polynomials. Zbl 1475.11054 Böttcher, Albrecht; Fukshansky, Lenny 2 2020 Spherical 2-designs and lattices from abelian groups. Zbl 1446.11128 Böttcher, Albrecht; Eisenbarth, Simon; Fukshansky, Lenny; Garcia, Stephan Ramon; Maharaj, Hiren 2 2019 The diversity and beauty of applied operator theory. Proceedings of the 28th international workshop on operator theory and its applications, IWOTA, Chemnitz, Germany 2017. Zbl 1396.47001 2 2018 Exploration of Toeplitz-like matrices with unbounded symbols is not a purely academic journey. Zbl 1482.47049 Böttcher, Albrecht; Garoni, Carlo; Serra-Capizzano, Stefano 15 2017 Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices. Zbl 1388.15028 Böttcher, Albrecht; Bogoya, Johan M.; Grudsky, Sergei M.; Maximenko, Egor A. 11 2017 Similarity between two projections. Zbl 1508.47021 Böttcher, Albrecht; Simon, Barry; Spitkovsky, Ilya 11 2017 The Duduchava-Roch formula. Zbl 1381.47020 Böttcher, Albrecht 3 2017 Addendum to: “Lattices from equiangular tight frames”. Zbl 1403.42033 Böttcher, Albrecht; Fukshansky, Lenny 2 2017 On the constants in Markov inequalities for the Laplace operator on polynomials with the Laguerre norm. Zbl 1365.41013 Böttcher, Albrecht; Rebs, Christian 1 2017 Eigenvectors of Hermitian Toeplitz matrices with smooth simple-loop symbols. Zbl 1331.47046 Bogoya, J. M.; Böttcher, A.; Grudsky, S. M.; Maximenko, E. A. 17 2016 From convergence in distribution to uniform convergence. Zbl 1419.60005 Bogoya, J. M.; Böttcher, A.; Maximenko, E. A. 8 2016 The limit of the zero set of polynomials of the Fibonacci type. Zbl 1405.11012 Böttcher, Albrecht; Kittaneh, Fuad 4 2016 Lattices from equiangular tight frames. Zbl 1403.42034 Böttcher, Albrecht; Fukshansky, Lenny; Garcia, Stephan Ramon; Maharaj, Hiren; Needell, Deanna 3 2016 On the symmetrization of general Wiener-Hopf operators. Zbl 1424.47046 Böttcher, A.; Speck, F.-O. 2 2016 Schatten class integral operators occurring in Markov-type inequalities. Zbl 1377.47009 Böttcher, Albrecht; Langenau, Holger; Widom, Harold 1 2016 Lattices from Hermitian function fields. Zbl 1334.11049 Böttcher, Albrecht; Fukshansky, Lenny; Garcia, Stephan Ramon; Maharaj, Hiren 1 2016 Eigenvalues of Hermitian Toeplitz matrices with smooth simple-loop symbols. Zbl 1302.65086 Bogoya, J. M.; Böttcher, A.; Grudsky, S. M.; Maximenko, E. A. 30 2015 Maximum norm versions of the Szegő and Avram-Parter theorems for Toeplitz matrices. Zbl 1320.15028 Bogoya, J. M.; Böttcher, A.; Grudsky, S. M.; Maximenko, E. A. 12 2015 Toeplitz determinants with perturbations in the corners. Zbl 1300.15010 Böttcher, Albrecht; Fukshansky, Lenny; Garcia, Stephan Ramon; Maharaj, Hiren 8 2015 On lattices generated by finite abelian groups. Zbl 1328.11077 Böttcher, Albrecht; Fukshansky, Lenny; Garcia, Stephan Ramon; Maharaj, Hiren 6 2015 Borodin-Okounkov and Szegő for Toeplitz operators on model spaces. Zbl 1312.47032 Böttcher, Albrecht 2 2014 A Newton method for canonical Wiener-Hopf and spectral factorization of matrix polynomials. Zbl 1303.47026 Böttcher, Albrecht; Halwass, Martin 10 2013 Wiener-Hopf and spectral factorization of real polynomials by Newton’s method. Zbl 1281.65075 Böttcher, Albrecht; Halwass, Martin 8 2013 The factorization problem: some known results and open questions. Zbl 1280.47027 Böttcher, Albrecht; Spitkovsky, Ilya M. 7 2013 Classification of the finite-dimensional algebras generated by two tightly coupled idempotents. Zbl 1285.16020 Böttcher, A.; Spitkovsky, I. M. 6 2013 Best constants for Markov type inequalities in Hilbert space norms. Zbl 1299.26044 Böttcher, Albrecht 4 2013 Preface. Zbl 1298.00102 1 2013 The index formula of Douglas for block Toeplitz operators on the Bergman space of the ball. Zbl 1283.47031 Böttcher, Albrecht; Perälä, Antti 1 2013 Asymptotics of individual eigenvalues of a class of large Hessenberg Toeplitz matrices. Zbl 1390.15094 Bogoya, J. M.; Böttcher, A.; Grudsky, S. M. 10 2012 Eigenvalues of Hermitian Toeplitz matrices with polynomially increasing entries. Zbl 1258.15011 Bogoya, Johan M.; Böttcher, Albrecht; Grudsky, Sergei M. 8 2012 Orthogonal and skew-symmetric operators in real Hilbert space. Zbl 1277.47022 Böttcher, Albrecht; Pietsch, Albrecht 7 2012 Eigenvectors of Hessenberg Toeplitz matrices and a problem by Dai, Geary, and Kadanoff. Zbl 1260.15009 Bogoya, J. M.; Böttcher, A.; Grudsky, S. M.; Maksimenko, E. A. 6 2012 Group inversion in certain finite-dimensional algebras generated by two idempotents. Zbl 1262.15018 Böttcher, A.; Spitkovsky, I. M. 5 2012 The Fox-Li operator as a test and a spur for Wiener-Hopf theory. Zbl 1317.47027 Böttcher, Albrecht; Grudsky, Sergei; Iserles, Arieh 5 2012 First-order trace formulae for the iterates of the Fox-Li operator. Zbl 1270.47024 Böttcher, Albrecht; Grudsky, Sergei; Huybrechs, Daan; Iserles, Arieh 4 2012 On certain finite-dimensional algebras generated by two idempotents. Zbl 1235.15017 Böttcher, A.; Spitkovsky, I. M. 9 2011 Spectral theory of large Wiener-Hopf operators with complex-symmetric kernels and rational symbols. Zbl 1227.47015 Böttcher, Albrecht; Grudsky, Sergei; Iserles, Arieh 9 2011 Eigenvalues of Hessenberg Toeplitz matrices generated by symbols with several singularities. Zbl 1207.47026 Bogoya, J. M.; Böttcher, A.; Grudsky, S. M.; Maksimenko, E. A. 5 2011 On the best constants in Markov-type inequalities involving Gegenbauer norms with different weights. Zbl 1222.41034 Böttcher, Albrecht; Dörfler, Peter 4 2011 Inequalities of the Markov type for partial derivatives of polynomials in several variables. Zbl 1221.41006 Böttcher, Albrecht; Dörfler, Peter 4 2011 A gentle guide to the basics of two projections theory. Zbl 1189.47073 Böttcher, A.; Spitkovsky, I. M. 105 2010 Inside the eigenvalues of certain Hermitian Toeplitz band matrices. Zbl 1195.15009 Böttcher, A.; Grudsky, S. M.; Maksimenko, E. A. 30 2010 Weighted Markov-type inequalities, norms of Volterra operators, and zeros of Bessel functions. Zbl 1186.41004 Böttcher, Albrecht; Dörfler, Peter 14 2010 On the singular values and eigenvalues of the Fox-Li and related operators. Zbl 1233.47022 Böttcher, Albrecht; Brunner, Hermann; Iserles, Arieh; Nørsett, Syvert P. 11 2010 On the structure of the eigenvectors of large Hermitian Toeplitz band matrices. Zbl 1267.47044 Böttcher, Albrecht; Grudsky, Sergei M.; Maksimenko, Egor A. 6 2010 Variable-coefficient Toeplitz matrices with symbols beyond the Wiener algebra. Zbl 1203.15019 Böttcher, Albrecht; Grudsky, Sergei 4 2010 On the best constants in Markov-type inequalities involving Laguerre norms with different weights. Zbl 1205.41024 Böttcher, Albrecht; Dörfler, Peter 3 2010 On the best constants in inequalities of the Markov and Wirtinger types for polynomials on the half-line. Zbl 1162.41004 Böttcher, Albrecht; Dörfler, Peter 12 2009 Drazin inversion in the von Neumann algebra generated by two orthogonal projections. Zbl 1178.47026 Böttcher, A.; Spitkovsky, I. M. 10 2009 The first order asymptotics of the extreme eigenvectors of certain Hermitian Toeplitz matrices. Zbl 1181.47023 Böttcher, A.; Grudsky, S.; Maksimenko, E. A.; Unterberger, J. 6 2009 Probabilistic spherical Marcinkiewicz-Zygmund inequalities. Zbl 1168.42002 Böttcher, Albrecht; Kunis, Stefan; Potts, Daniel 5 2009 On the asymptotics of all eigenvalues of Hermitian Toeplitz band matrices. Zbl 1181.15010 Böttcher, A.; Grudsky, S. M.; Maksimenko, E. A. 4 2009 Some problems concerning the test functions in the Szegő and Avram-Parter theorems. Zbl 1168.47023 Böttcher, Albrecht; Grudsky, Sergei; Schwartz, Moshe 3 2009 The Frobenius norm and the commutator. Zbl 1173.15010 Böttcher, Albrecht; Wenzel, David 43 2008 Pushing the envelope of the test functions in the Szegö and Avram-Parter theorems. Zbl 1153.15012 Böttcher, Albrecht; Grudsky, Sergei M.; Maksimenko, Egor A. 5 2008 Uniform boundedness of Toeplitz matrices with variable coefficients. Zbl 1155.47029 Böttcher, Albrecht; Grudsky, Sergei 4 2008 The Szegő and Avram-Parter theorems for general test functions. Zbl 1145.15007 Böttcher, Albrecht; Grudsky, Sergei M.; Maksimenko, Egor A. 4 2008 Orthogonal symmetric Toeplitz matrices. Zbl 1157.47021 Böttcher, Albrecht 3 2008 Asymptotic pseudomodes of Toeplitz matrices. Zbl 1172.47021 Böttcher, Albrecht; Grudsky, Sergei; Unterberger, Jérémie 1 2008 Functions of banded Hermitian block Toeplitz matrices in signal processing. Zbl 1115.47059 Gutiérrez-Gutiérrez, Jesús; Crespo, Pedro M.; Böttcher, Albrecht 13 2007 Norms of Toeplitz matrices with Fisher–Hartwig symbols. Zbl 1145.47023 Böttcher, Albrecht; Virtanen, Jani 7 2007 Mass concentration in quasicommutators of Toeplitz matrices. Zbl 1128.47063 Böttcher, Albrecht; Gutiérrez-Gutiérrez, Jesús; Crespo, Pedro M. 7 2007 Probability against condition number and sampling of multivariate trigonometric random polynomials. Zbl 1171.65389 Böttcher, Albrecht; Potts, Daniel 7 2007 Generalized Krein algebras and asymptotics of Toeplitz determinants. Zbl 1144.47311 Böttcher, A.; Karlovich, A.; Silbermann, B. 2 2007 A probability argument in favor of ignoring small singular values. Zbl 1120.65055 Boettcher, Albrecht; Potts, Daniel; Wenzel, David 2 2007 Analysis of Toeplitz operators. Prepared jointly with Alexei Karlovich. 2nd ed. Zbl 1098.47002 Böttcher, Albrecht; Silbermann, Bernd 275 2006 Convergence rates for Tikhonov regularization from different kinds of smoothness conditions. Zbl 1110.65041 Böttcher, Albrecht; Hofmann, Bernd; Tautenhahn, Ulrich; Yamamoto, Masahiro 25 2006 From Toeplitz eigenvalues through Green’s kernels to higher-order Wirtinger-Sobolev inequalities. Zbl 1118.47016 Böttcher, Albrecht; Widom, Harold 22 2006 Szegő via Jacobi. Zbl 1116.47024 Böttcher, Albrecht; Widom, Harold 18 2006 On the eigenvalues of certain canonical higher-order ordinary differential operators. Zbl 1110.34060 Böttcher, Albrecht; Widom, Harold 6 2006 On the asymptotic behavior of the eigenvectors of large banded Toeplitz matrices. Zbl 1101.47015 Böttcher, A.; Grudsky, S.; Ramírez de Arellano, E. 5 2006 On the problem of testing the structure of a matrix by displacement operations. Zbl 1117.65058 Böttcher, Albrecht 2 2006 On the verification of linear equations and the identification of the Toeplitz-plus-Hankel structure. Zbl 1126.47027 Böttcher, Albrecht; Wenzel, David 1 2006 Schatten norms of Toeplitz matrices with Fisher–Hartwig singularities. Zbl 1140.47310 Böttcher, Albrecht 1 2006 Minimum distance to the range of a banded lower triangular Toeplitz operator in \(\ell^1\) and application in \(\ell^1\)-optimal control. Zbl 1116.47025 Hurák, Zdeněk; Böttcher, Albrecht; Šebek, Michael 1 2006 Spectral properties of banded Toeplitz matrices. Zbl 1089.47001 Böttcher, Albrecht; Grudsky, Sergei M. 192 2005 How big can the commutator of two matrices be and how big is it typically? Zbl 1077.15020 Böttcher, Albrecht; Wenzel, David 41 2005 Structured condition numbers of large Toeplitz matrices are rarely better than usual condition numbers. Zbl 1164.15309 Böttcher, A.; Grudsky, S. M. 22 2005 Two elementary derivations of the pure Fisher–Hartwig determinant. Zbl 1081.47033 Böttcher, Albrecht; Widom, Harold 14 2005 The first Szegő limit theorem for non-selfadjoint operators in the Følner algebra. Zbl 1094.47039 Böttcher, Albrecht; Otte, Peter 5 2005 The constants in the asymptotic formulas by Rambour and Seghier for inverses of Toeplitz matrices. Zbl 1070.47015 Böttcher, A. 10 2004 Transient behavior of powers and exponentials of large Toeplitz matrices. Zbl 1085.47033 Böttcher, Albrecht 2 2004 Topics in the numerical linear algebra of Toeplitz and Hankel matrices. Zbl 1093.47028 Böttcher, Albrecht; Rost, Karla 2 2004 Algebras of Toeplitz operators with oscillating symbols. Zbl 1083.47023 Böttcher, Albrecht; Grudsky, Sergei M.; Ramírez de Arellano, Enrique 1 2004 Asymptotically good pseudomodes for Toeplitz matrices and Wiener-Hopf operators. Zbl 1073.47036 Böttcher, Albrecht; Grudsky, Sergei 1 2004 The spectra of large Toeplitz band matrices with a randomly perturbed entry. Zbl 1022.47019 Böttcher, A.; Embree, M.; Sokolov, V. I. 9 2003 The \(C^{*}\)-algebra of singular integral operators with semi-almost periodic coefficients. Zbl 1048.47027 Böttcher, A.; Karlovich, Yu. I.; Spitkovsky, I. M. 9 2003 On large Toeplitz band matrices with an uncertain block. Zbl 1021.15008 Böttcher, A.; Embree, M.; Sokolov, V. I. 7 2003 Block Toeplitz operators with frequency-modulated semi-almost periodic symbols. Zbl 1036.47014 Böttcher, A.; Grudsky, S.; Spitkovsky, I. 5 2003 Asymptotic spectra of dense Toeplitz matrices are unstable. Zbl 1038.65030 Böttcher, A.; Grudsky, S. M. 5 2003 ...and 97 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,508 Authors 93 Böttcher, Albrecht 77 Serra-Capizzano, Stefano 57 Karlovich, Yuri I. 46 Silbermann, Bernd 43 Grudsky, Sergei Mikhailovich 43 Spitkovsky, Ilya Matvey 40 Karlovych, Oleksiy 28 Garoni, Carlo 27 Ehrhardt, Torsten 27 Roch, Steffen 20 Basor, Estelle L. 17 Câmara, Maria Cristina 16 Shargorodsky, Eugene 15 Maksimenko, Egor A. 14 Bini, Dario Andrea 14 Sesana, Debora 13 Garcia, Stephan Ramon 13 Lindner, Marko 13 Rabinovich, Vladimir Samuilovich 13 Sharma, Basant Lal 12 Bastos, Maria Amélia 12 Pinheiro de Castro, Luís Filipe 12 Deng, Chunyuan 12 Fernandes, Claudio A. 11 Ekström, Sven-Erik 11 Rambour, Philippe 11 Rodman, Leiba X. 11 Seidel, Markus 10 Barbarino, Giovanni 10 Bogoya, Manuel 10 Cheng, Cheman 10 Didenko, Victor D. 10 Donatelli, Marco 10 Fukshansky, Lenny 10 Hansen, Anders C. 10 Jafarov, Sadulla Z. 10 Meini, Beatrice 10 Widom, Harold 9 Colbrook, Matthew J. 9 Hwang, In Sung 9 Kumar, V. B. Kiran 9 Lee, Woo Young 9 Mazza, Mariarosa 9 Ran, André C. M. 9 Santos, Pedro A. 8 Bogoya, Johan M. 8 Chandler-Wilde, Simon N. 8 Hofmann, Bernd 8 Its, Alexander Rudolfovich 8 Lebre, Amarino Brites 8 Li, Yuan 8 Saker, Samir H. 8 Virtanen, Jani A. 8 Xu, Qingxiang 7 Gu, Caixing 7 Jasiczak, Michał 7 Kokilashvili, Vakhtang 7 Krupnik, Naum Yakovlevich 7 Noschese, Silvia 7 Seghier, Abdellatif 7 Speck, Frank-Olme 7 Speleers, Hendrik 7 Tierz, Miguel 7 Wang, Hong 6 Charlier, Christophe 6 Chruściński, Dariusz 6 Curto, Raúl Enrique 6 dos Santos, António Ferreira 6 Gharakhloo, Roozbeh 6 Kaashoek, Marinus Adriaan 6 Manni, Carla 6 Mathé, Peter 6 Namboodiri, M. N. N. 6 Reichel, Lothar 6 Samko, Stefan Grigor’evich 6 Shi, Weijuan 6 Simon, Barry 6 Stukopin, Vladimir Alekseevich 6 Tablino Possio, Cristina 6 Vassalos, Paris 6 Wei, Yimin 5 Agarwal, Ravi P. 5 Aschbacher, Walter H. 5 Avsyankin, Oleg Gennadievich 5 Bianchi, Davide 5 Bourget, Alain 5 Davies, Edward Brian 5 Deift, Percy A. 5 Dhara, Kousik 5 Duits, Maurice 5 Dym, Harry 5 Embree, Mark 5 Fikioris, George 5 Ginovyan, Mamikon S. 5 Junghanns, Peter 5 Kang, Dong-Oh 5 Kimura, Gen 5 Kulkarni, Sudhir Hanmantrao 5 Maharaj, Hiren 5 Mascarenhas, Helena ...and 1,408 more Authors all top 5 Cited in 345 Serials 197 Linear Algebra and its Applications 93 Integral Equations and Operator Theory 69 Journal of Mathematical Analysis and Applications 54 Journal of Functional Analysis 29 Complex Analysis and Operator Theory 20 Journal of Computational and Applied Mathematics 20 Numerical Linear Algebra with Applications 18 Mathematische Nachrichten 15 Communications in Mathematical Physics 15 Journal of Approximation Theory 14 Linear and Multilinear Algebra 13 Proceedings of the American Mathematical Society 12 Advances in Mathematics 11 Journal of Statistical Physics 11 Mathematics of Computation 11 Automatica 11 Numerische Mathematik 11 Transactions of the American Mathematical Society 11 Journal of Integral Equations and Applications 11 Banach Journal of Mathematical Analysis 10 Mathematical Notes 10 Zeitschrift für Analysis und ihre Anwendungen 10 Constructive Approximation 10 Numerical Algorithms 10 ELA. 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Mathématiques. Série VI 4 SIAM Journal on Scientific Computing 4 Applied and Computational Harmonic Analysis 4 St. Petersburg Mathematical Journal 4 Annales Henri Poincaré 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Mediterranean Journal of Mathematics 4 Concrete Operators 3 Nonlinearity 3 Rocky Mountain Journal of Mathematics 3 Acta Scientiarum Mathematicarum 3 Bulletin of the London Mathematical Society 3 Duke Mathematical Journal 3 Journal of Statistical Planning and Inference 3 Mathematische Zeitschrift 3 Memoirs of the American Mathematical Society 3 Systems & Control Letters 3 Bulletin of the Iranian Mathematical Society ...and 245 more Serials all top 5 Cited in 58 Fields 781 Operator theory (47-XX) 488 Linear and multilinear algebra; matrix theory (15-XX) 320 Numerical analysis (65-XX) 233 Functional analysis (46-XX) 143 Harmonic analysis on Euclidean spaces (42-XX) 133 Integral equations (45-XX) 126 Functions of a complex variable (30-XX) 115 Partial differential equations (35-XX) 110 Probability theory and stochastic processes (60-XX) 72 Quantum theory (81-XX) 66 Approximations and expansions (41-XX) 61 Statistical mechanics, structure of matter (82-XX) 52 Statistics (62-XX) 34 Number theory (11-XX) 33 Real functions (26-XX) 32 Information and communication theory, circuits (94-XX) 31 Special functions (33-XX) 31 Systems theory; control (93-XX) 30 Combinatorics (05-XX) 26 Ordinary differential equations (34-XX) 23 Computer science (68-XX) 21 Dynamical systems and ergodic theory (37-XX) 20 Mechanics of deformable solids (74-XX) 19 Difference and functional equations (39-XX) 19 Abstract harmonic analysis (43-XX) 17 Optics, electromagnetic theory (78-XX) 15 Several complex variables and analytic spaces (32-XX) 15 Operations research, mathematical programming (90-XX) 14 Differential geometry (53-XX) 13 Integral transforms, operational calculus (44-XX) 13 Fluid mechanics (76-XX) 11 Associative rings and algebras (16-XX) 11 Group theory and generalizations (20-XX) 10 Potential theory (31-XX) 10 Global analysis, analysis on manifolds (58-XX) 9 History and biography (01-XX) 9 Sequences, series, summability (40-XX) 8 Algebraic geometry (14-XX) 8 Topological groups, Lie groups (22-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Field theory and polynomials (12-XX) 7 Convex and discrete geometry (52-XX) 7 General topology (54-XX) 6 Nonassociative rings and algebras (17-XX) 6 Measure and integration (28-XX) 5 \(K\)-theory (19-XX) 4 Biology and other natural sciences (92-XX) 3 Geometry (51-XX) 2 Mathematical logic and foundations (03-XX) 2 Commutative algebra (13-XX) 2 Algebraic topology (55-XX) 2 Relativity and gravitational theory (83-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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