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## Kuchment, Peter A.

Compute Distance To:
 Author ID: kuchment.peter-a Published as: Kuchment, P.; Kuchment, P. A.; Kuchment, Peter; Kuchment, Peter A.
 Documents Indexed: 150 Publications since 1972, including 14 Books Reviewing Activity: 1 Review
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#### Co-Authors

 53 single-authored 8 Kunyansky, Leonid A. 7 Semënov, Evgeniĭ Mikhaĭlovich 6 Agranovsky, Mark L. 5 Pan’kov, Andreĭ Anatol’evich 4 Berkolaiko, Gregory 4 Figotin, Alex 4 Sunada, Toshikazu 3 Braverman, Maxim 3 Do, Ngoc T. 3 Exner, Pavel 3 Fulling, Stephen A. 3 Kreĭn, Selim Grigor’evich 3 Maz’ya, Vladimir Gilelevich 3 Novikov, Sergeĭ Petrovich 3 Ong, Beng-Seong 3 Quinto, Eric Todd 3 Terzioglu, Fatma 3 Vaĭnberg, Boris Rufimovich 2 Aguilar, Valentina 2 Ambartsoumian, Gaik 2 Bukhshtaber, Viktor Matveevich 2 Finch, David V. 2 Fridman, Buma L. 2 Friedlander, Leonid 2 Gromov, Mikhael Leonidovich 2 Hristova, Yulia 2 Ivrii, Victor Ja. 2 Keating, Jonathan P. 2 Kha, Minh 2 Kordyukov, Yuri A. 2 Lancaster, Kirk E. 2 Levendorskiĭ, Sergeĭ Zakharovich 2 Lin, Vladimir Ya. 2 L’Vin, Sergej Ya. 2 Lvin, Sergey J. 2 Pankov, Alexander A. 2 Pinchover, Yehuda 2 Raich, Andrew S. 2 Steinhauer, Dustin 2 Struppa, Daniele Carlo 2 Teplyaev, Alexander 2 Winn, Brian 2 Zaidenberg, Mikhail G. 1 Allmaras, Moritz 1 Auckly, David R. 1 Axmann, Waldemar 1 Baines, W. 1 Bal, Guillaume 1 Baras, John S. 1 Benchama, Noureddine 1 Berenstein, Carlos Alberto 1 Berezans’kyĭ, Yuriĭ Makarovych 1 Carlson, Robert C. 1 Carroll, Raymond James 1 Chang, Der-Chen E. 1 Cheney, Margaret 1 Corbin, James E. 1 Darrow, David 1 Dikansky, Arnold 1 Egorov, Yuriĭ Vladimirovich 1 Ehrenpreis, Leon 1 Farkas, Hershel M. 1 Figotin, Alexander 1 Freidlin, Mark I. 1 Friedlander, L. F. 1 Gay, Roger 1 Gindikin, Simon Grigorevich 1 Harrison, Jon M. 1 Kanschat, Guido 1 Kappeler, Thomas 1 Kawai, Takahiro 1 Khovanskiĭ, Askold Georgievich 1 Komech, Aleksandr I. 1 Krasnenker, A. S. 1 Kutateladze, Semën Samsonovich 1 Lakshtanov, Evgeny L. 1 Li, Baoqin 1 Lissianoi, Serguei 1 Ma, Daowei 1 Mallick, Bani K. 1 McOwen, Robert C. 1 Mogilevskaya, Lyudmila 1 Mogilevsky, Mila 1 Molchanov, Stanislav Alekseevich 1 Napoletani, Domenico 1 Nguyen, Linh Anh 1 Novikov, Roman G. 1 Ovchinnikov, Vladimir I. 1 Papanicolaou, Vassilis G. 1 Post, Olaf 1 Ragusa, Jean C. 1 Reshetnyak, Yuriĭ Grigor’evich 1 Sabadini, Irene 1 Schotland, John C. 1 Sebbar, Ahmed 1 Shneiberg, Iosiph 1 Sklyadnev, S. A. 1 Smilansky, Uzy 1 Sobolev, Alexander V. 1 Sottile, Frank ...and 15 more Co-Authors
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#### Serials

 11 Inverse Problems 8 Russian Mathematical Surveys 7 Soviet Mathematics. Doklady 6 Contemporary Mathematics 5 Functional Analysis and its Applications 4 Journal of Physics A: Mathematical and Theoretical 4 Inverse Problems and Imaging 3 Uspekhi Matematicheskikh Nauk [N. S.] 3 Waves in Random Media 3 Akademiya Nauk Moldavskoĭ SSR. Ordena Trudovogo Krasnogo Znameni Institut Matematiki s Vychislitel’nym Tsentrom. Matematicheskie Issledovaniya 3 SIAM Journal on Applied Mathematics 3 Notices of the American Mathematical Society 2 Applicable Analysis 2 Communications in Mathematical Physics 2 Journal of Mathematical Physics 2 Journal of Functional Analysis 2 Matematicheskiĭ Sbornik. Novaya Seriya 2 Mathematics of the USSR. Izvestiya 2 Transactions of the American Mathematical Society 2 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 2 Mathematics of the USSR, Sbornik 2 Bulletin of the American Mathematical Society. New Series 1 American Mathematical Monthly 1 Journal d’Analyse Mathématique 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Differentsial’nye Uravneniya 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Journal of Differential Equations 1 Kibernetika 1 Mathematische Nachrichten 1 Acta Applicandae Mathematicae 1 European Journal of Applied Mathematics 1 The Journal of Geometric Analysis 1 Geometric and Functional Analysis. GAFA 1 Communications in Partial Differential Equations 1 Journal of Physics A: Mathematical and General 1 SIAM Journal on Mathematical Analysis 1 Experimental Mathematics 1 Memoirs on Differential Equations and Mathematical Physics 1 Advances in Computational Mathematics 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Lecture Notes in Mathematics 1 Mathematical Surveys and Monographs 1 Proceedings of Symposia in Pure Mathematics 1 Complex Analysis and Operator Theory 1 SIAM Journal on Imaging Sciences 1 Journal of Spectral Theory 1 Optimizacija 1 Analysis and Mathematical Physics 1 Nanoscale Systems: Mathematical Modeling, Theory and Applications 1 Operator Theory: Advances and Applications 1 Translations. Series 2. American Mathematical Society
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#### Fields

 75 Partial differential equations (35-XX) 29 Biology and other natural sciences (92-XX) 27 Operator theory (47-XX) 26 Quantum theory (81-XX) 24 Integral transforms, operational calculus (44-XX) 24 Global analysis, analysis on manifolds (58-XX) 21 Numerical analysis (65-XX) 20 Optics, electromagnetic theory (78-XX) 16 History and biography (01-XX) 12 General and overarching topics; collections (00-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Ordinary differential equations (34-XX) 8 Combinatorics (05-XX) 7 Functional analysis (46-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Differential geometry (53-XX) 6 Algebraic topology (55-XX) 5 Abstract harmonic analysis (43-XX) 5 Manifolds and cell complexes (57-XX) 4 Mechanics of deformable solids (74-XX) 4 Information and communication theory, circuits (94-XX) 3 Functions of a complex variable (30-XX) 3 Approximations and expansions (41-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Computer science (68-XX) 3 Fluid mechanics (76-XX) 2 Topological groups, Lie groups (22-XX) 2 Difference and functional equations (39-XX) 2 Geometry (51-XX) 2 General topology (54-XX) 2 Operations research, mathematical programming (90-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX)

#### Citations contained in zbMATH Open

103 Publications have been cited 2,232 times in 1,195 Documents Cited by Year
Introduction to quantum graphs. Zbl 1318.81005
Berkolaiko, Gregory; Kuchment, Peter
2013
Floquet theory for partial differential equations. Zbl 0789.35002
Kuchment, Peter
1993
Quantum graphs. I: Some basic structures. Zbl 1063.81058
Kuchment, Peter
2004
Quantum graphs. II: Some spectral properties of quantum and combinatorial graphs. Zbl 1070.81062
Kuchment, Peter
2005
Mathematics of thermoacoustic tomography. Zbl 1185.35327
Kuchment, Peter; Kunyansky, Leonid
2008
Graph models for waves in thin structures. Zbl 1063.35525
Kuchment, Peter
2002
On the spectra of carbon nano-structures. Zbl 1145.81032
Kuchment, Peter; Post, Olaf
2007
The mathematics of photonic crystals. Zbl 0986.78004
Kuchment, Peter
2001
Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media. Zbl 1180.35563
Hristova, Yulia; Kuchment, Peter; Nguyen, Linh
2008
Band-gap structure of spectra of periodic dielectric and acoustic media. I: Scalar model. Zbl 0852.35014
Figotin, Alex; Kuchment, Peter
1996
Floquet theory for partial differential equations. Zbl 0519.35003
Kuchment, P. A.
1982
Quantum graphs and their applications. Proceedings of an AMS-IMS-SIAM joint summer research conference on quantum graphs and their applications, Snowbird, UT, USA, June 19–23, 2005. Zbl 1098.81007
Berkolaiko, Gregory (ed.); Carlson, Robert (ed.); Fulling, Stephen A. (ed.); Kuchment, Peter (ed.)
2006
An overview of periodic elliptic operators. Zbl 1346.35170
Kuchment, Peter
2016
Band-gap structure of spectra of periodic dielectric and acoustic media. II: Two-dimensional photonic crystals. Zbl 0868.35009
Figotin, A.; Kuchment, P.
1996
Analysis on graphs and its applications. Selected papers based on the Isaac Newton Institute for Mathematical Sciences programme, Cambridge, UK, January 8–June 29, 2007. Zbl 1143.05002
Exner, Pavel (ed.); Keating, Jonathan P. (ed.); Kuchment, Peter (ed.); Sunada, Toshikazu (ed.); Teplyaev, Alexander (ed.)
2008
The Radon transform and medical imaging. Zbl 1282.92001
Kuchment, Peter
2014
Quantum graphs: an introduction and a brief survey. Zbl 1210.05169
Kuchment, Peter
2008
An efficient finite element method for computing spectra of photonic and acoustic band-gap materials. I: Scalar case. Zbl 0963.78028
Axmann, Waldemar; Kuchment, Peter
1999
Convergence of spectra of mesoscopic systems collapsing onto a graph. Zbl 0982.35076
Kuchment, Peter; Zeng, Hongbiao
2001
Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths. Zbl 1317.81127
Berkolaiko, G.; Kuchment, P.
2012
Spectral properties of classical waves in high-contrast periodic media. Zbl 0916.35011
Figotin, A.; Kuchment, P.
1998
Mathematics of photoacoustic and thermoacoustic tomography. Zbl 1259.92065
Kuchment, Peter; Kunyansky, Leonid
2011
Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed. Zbl 1126.35087
Agranovsky, Mark; Kuchment, Peter
2007
Stabilizing inverse problems by internal data. Zbl 1252.92037
Kuchment, Peter; Steinhauer, Dustin
2012
Banach bundles and linear operators. Zbl 0335.47017
Zaĭdenberg, M. G.; Kreĭn, S. G.; Kuchment, P. A.; Pankov, A. A.
1975
Approximation by spherical waves in $$L^p$$-spaces. Zbl 0898.44003
Agranovsky, Mark; Berenstein, Carlos; Kuchment, Peter
1996
Index theorems for quantum graphs. Zbl 1127.58027
Fulling, S. A.; Kuchment, P.; Wilson, J. H.
2007
On occurrence of spectral edges for periodic operators inside the Brillouin zone. Zbl 1141.82340
Harrison, Jon M.; Kuchment, P.; Sobolev, A.; Winn, B.
2007
Range descriptions for the spherical mean Radon transform. Zbl 1132.44002
Agranovsky, Mark; Kuchment, Peter; Quinto, Eric Todd
2007
Asymptotics of spectra of Neumann Laplacians in thin domains. Zbl 1050.35094
Kuchment, Peter; Zeng, Honbiao
2003
A range description for the planar circular Radon transform. Zbl 1120.44003
Ambartsoumian, Gaik; Kuchment, Peter
2007
Mathematics of hybrid imaging: A brief review. Zbl 1248.65102
Kuchment, Peter
2012
On the injectivity of the circular Radon transform. Zbl 1072.44001
Ambartsoumian, Gaik; Kuchment, Peter
2005
On local tomography. Zbl 0832.44001
Kuchment, Peter; Lancaster, Kirk; Mogilevskaya, Lyudmila
1995
On the structure of spectra of periodic elliptic operators. Zbl 1058.35174
Kuchment, Peter; Levendorskiĭ, Sergei
2002
Integral representations and Liouville theorems for solutions of periodic elliptic equations. Zbl 0986.35028
Kuchment, Peter; Pinchover, Yehuda
2001
On absence of embedded eigenvalues for Schrödinger operators with perturbed periodic potentials. Zbl 0960.35077
Kuchment, Peter; Vainberg, Boris
2000
Quantum graph spectra of a graphyne structure. Zbl 1273.81067
Do, Ngoc T.; Kuchment, Peter
2013
Detecting small low emission radiating sources. Zbl 1266.82083
Allmaras, Moritz; Darrow, David; Hristova, Yulia; Kanschat, Guido; Kuchment, Peter
2013
On the location of spectral edges in $$\mathbb Z$$-periodic media. Zbl 1204.81063
Exner, Pavel; Kuchment, Peter; Winn, Brian
2010
Spectral properties of high contrast band-gap materials and operators on graphs. Zbl 0930.35112
Kuchment, Peter; Kunyansky, Leonid A.
1999
Banach bundles and linear operators. Zbl 0317.47018
Zaĭdenberg, M. G.; Kreĭn, S. G.; Kuchment, P. A.; Pankov, A. A.
1975
On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators. Zbl 1125.39021
Kuchment, Peter; Vainberg, Boris
2006
Compton camera imaging and the cone transform: a brief overview. Zbl 06897197
Terzioglu, Fatma; Kuchment, Peter; Kunyansky, Leonid
2018
Liouville theorems and spectral edge behavior on Abelian coverings of compact manifolds. Zbl 1127.58015
Kuchment, Peter; Pinchover, Yehuda
2007
Differential operators on graphs and photonic crystals. Zbl 0993.65122
Kuchment, P.; Kunyansky, L.
2002
Mathematics of photoacoustic and thermoacoustic tomography. Zbl 1331.92076
Kuchment, Peter; Kunyansky, Leonid
2015
2D and 3D reconstructions in acousto-electric tomography. Zbl 1217.35211
Kuchment, Peter; Kunyansky, Leonid
2011
Three-dimensional image reconstruction from Compton camera data. Zbl 1354.44002
Kuchment, Peter; Terzioglu, Fatma
2016
Reconstruction of a continuous representation with respect to a subrepresentation and a factor representation. Zbl 0332.46047
Kuchment, P. A.
1976
Range conditions for a spherical mean transform. Zbl 1190.44001
Agranovsky, Mark; Finch, David; Kuchment, Peter
2009
Tight frames of exponentially decaying Wannier functions. Zbl 1154.82028
Kuchment, Peter
2009
Inversion of weighted divergent beam and cone transforms. Zbl 1372.44004
Kuchment, Peter; Terzioglu, Fatma
2017
Stabilizing inverse problems by internal data. II: Non-local internal data and generic linearized uniqueness. Zbl 1330.35427
Kuchment, Peter; Steinhauer, Dustin
2015
One some spectral problems of mathematical physics. Zbl 1061.35065
Kuchment, Peter
2004
Critical partitions and nodal deficiency of billiard eigenfunctions. Zbl 1308.35152
Berkolaiko, Gregory; Kuchment, Peter; Smilansky, Uzy
2012
Synthetic focusing in ultrasound modulated tomography. Zbl 1286.44002
Kuchment, Peter; Kunyansky, Leonid
2010
Generalized transforms of Radon type and their applications. Zbl 1118.44001
Kuchment, Peter
2006
On guided waves in photonic crystal waveguides. Zbl 1046.35081
Kuchment, Peter; Ong, BengSeong
2003
On the Floquet theory of periodic difference equations. Zbl 0979.39011
Kuchment, P. A.
1991
Green’s function asymptotics near the internal edges of spectra of periodic elliptic operators: Spectral edge case. Zbl 1257.35080
Kuchment, Peter; Raich, Andrew
2012
A Bayesian approach to the detection of small low emission sources. Zbl 1228.62035
Xun, Xiaolei; Mallick, Bani; Carroll, Raymond J.; Kuchment, Peter
2011
Some inversion formulas in the single photon emission computed tomography. Zbl 0839.44002
Kuchment, Peter; Shneiberg, Iosiph
1994
Green’s function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior. Zbl 1394.35297
Kha, Minh; Kuchment, Peter; Raich, Andrew
2017
Differential and pseudo-differential operators on graphs as models of mesoscopic systems. Zbl 1200.82086
Kuchment, Peter
2003
On embedding eigenvalues of perturbed periodic Schrödinger operators. Zbl 0902.35077
Kuchment, Peter; Vainberg, Boris
1998
Range conditions for the exponential Radon transform. Zbl 0858.44002
Aguilar, Valentina; Ehrenpreis, Leon; Kuchment, Peter
1996
Vladimir A. Geyler, April 29, 1943–April 2, 2007. Zbl 1190.01017
Exner, Pavel; Keating, Jonathan P.; Kuchment, Peter; Sunada, Toshikazu; Teplyaev, Alexander
2008
Numerical harmonic analysis on the hyperbolic plane. Zbl 1022.65145
Fridman, Buma; Kuchment, Peter; Lancaster, Kirk; Lissianoi, Serguei; Mogilevsky, Mila
2000
Paley-Wiener theorem for exponential Radon transform. Zbl 0705.44001
Kuchment, Peter A.; L’Vin, Sergej Ya.
1990
On the question of the affine-invariant points of convex bodies. Zbl 0263.52004
Kuchment, P. A.
1972
On guided electromagnetic waves in photonic crystal waveguides. Zbl 1217.35181
Kuchment, Peter; Ong, Beng-Seong
2010
Solution of the linearized inverse conductivity problem in a half space via integral geometry. Zbl 0904.35096
Fridman, Buma; Kuchment, Peter; Ma, Daowei; Papanicolaou, Vassilis G.
1998
Range conditions for the multidimensional exponential x-ray transform. Zbl 0843.44005
Aguilar, Valentina; Kuchment, Peter
1995
Band-gap structure of the spectrum of periodic Maxwell operators. Zbl 0946.82517
Figotin, Alexander; Kuchment, Peter
1994
The range of the exponential Radon transform. Zbl 0748.44002
Kuchment, P. A.; L’vin, S. Ya.
1990
The support theorem for the single radius spherical mean transform. Zbl 1254.44001
Agranovsky, M.; Kuchment, P.
2011
Waves in periodic and random media. Proceedings of an AMS-IMS-SIAM joint summer research conference, South Hadley, MA, USA, June 22–28, 2002. Zbl 1029.00026
Kuchment, Peter (ed.)
2003
Iosif Shneiberg, July 26, 1950 - July 21, 1992. Zbl 0938.01043
Krein, Selim; Kuchment, Peter; Ovchinnikov, Vladimir; Semenov, Evgeny
1999
2D photonic crystals with cubic structure: Asymptotic analysis. Zbl 0901.65078
Figotin, A.; Kuchment, P.
1998
On inversion and range characterization of one transform arising in emission tomography. Zbl 0823.44007
Kuchment, P.
1994
Tomography, impedance imaging, and integral geometry. 1993 AMS-SIAM summer seminar, June 7-18, 1993, Mount Holyoke College, South Hadley, MA,, USA. Zbl 0801.00052
Quinto, Eric Todd (ed.); Cheney, Margaret (ed.); Kuchment, Peter (ed.)
1994
On the behavior of Floquet exponents of a kind of periodic evolution problems. Zbl 0792.35026
Kuchment, Peter
1994
Floquet representation of solutions of linear hypoelliptic systems of partial differential equations. Zbl 0414.35020
Kuchment, P. A.
1979
Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs. Zbl 1422.81110
Kuchment, Peter; Zhao, Jia
2019
On Parseval frames of exponentially decaying composite Wannier functions. Zbl 1428.35417
Auckly, David; Kuchment, Peter
2018
Identities for $$\sin x$$ that came from medical imaging. Zbl 1278.33001
Kuchment, Peter; Lvin, Sergey
2013
Remembering Leon Ehrenpreis (1930–2010). Zbl 1225.01086
Struppa, Daniele C.; Farkas, Hershel; Kawai, Takahiro; Kuchment, Peter; Quinto, Eric Todd; Sternberg, Shlomo; Taylor, Alan
2011
Spectral theory and geometric analysis. International conference in honor of Mikhail Shubin’s 65th birthday, Northeastern University, Boston, MA, USA, July 29 – August 2, 2009. Zbl 1207.58001
Braverman, Maxim (ed.); Friedlander, Leonid (ed.); Kappeler, Thomas (ed.); Kuchment, Peter (ed.); Topalov, Peter (ed.); Weitsman, Jonathan (ed.)
2011
Integral representations of solutions of periodic elliptic equations. Zbl 1133.35033
Kuchment, Peter
2007
Coincidence of length spectra does not imply isospectrality. Zbl 1083.35077
Fulling, S. A.; Kuchment, Peter
2005
Special issue: Dedicated to Professor Robert Brooks. Zbl 1076.81500
Kuchment, P. (ed.)
2004
On absolute continuity of spectra of periodic elliptic operators. Zbl 0965.35100
Kuchment, Peter; Levendorskiǐ, Sergei
1999
Voronezh winter mathematical schools. Dedicated to Selim Krein. Zbl 0997.00561
Kuchment, Peter (ed.); Lin, Vladimir (ed.)
1998
On positivity problems for the Radon transform and some related transforms. Zbl 0785.44003
Kuchment, Peter
1992
Spherical representation of solutions of invariant differential equations on a symmetric Riemannian space of noncompact type. Zbl 0593.58044
Kuchment, P. A.
1985
Representations of solutions of periodic partial differential equations. Zbl 0529.35009
Kuchment, P. A.
1983
Representations of solutions of invariant differential equations on certain symmetric spaces. Zbl 0497.58025
Kuchment, P. A.
1981
The absence of $$L_ 2-$$solutions for periodic partial differential equations. Zbl 0461.35029
Kuchment, P. A.
1980
Bloch solutions of periodic partial differential equations. Zbl 0459.35028
Kuchment, P. A.
1980
Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs. Zbl 1422.81110
Kuchment, Peter; Zhao, Jia
2019
Compton camera imaging and the cone transform: a brief overview. Zbl 06897197
Terzioglu, Fatma; Kuchment, Peter; Kunyansky, Leonid
2018
On Parseval frames of exponentially decaying composite Wannier functions. Zbl 1428.35417
Auckly, David; Kuchment, Peter
2018
Inversion of weighted divergent beam and cone transforms. Zbl 1372.44004
Kuchment, Peter; Terzioglu, Fatma
2017
Green’s function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior. Zbl 1394.35297
Kha, Minh; Kuchment, Peter; Raich, Andrew
2017
An overview of periodic elliptic operators. Zbl 1346.35170
Kuchment, Peter
2016
Three-dimensional image reconstruction from Compton camera data. Zbl 1354.44002
Kuchment, Peter; Terzioglu, Fatma
2016
Mathematics of photoacoustic and thermoacoustic tomography. Zbl 1331.92076
Kuchment, Peter; Kunyansky, Leonid
2015
Stabilizing inverse problems by internal data. II: Non-local internal data and generic linearized uniqueness. Zbl 1330.35427
Kuchment, Peter; Steinhauer, Dustin
2015
The Radon transform and medical imaging. Zbl 1282.92001
Kuchment, Peter
2014
Introduction to quantum graphs. Zbl 1318.81005
Berkolaiko, Gregory; Kuchment, Peter
2013
Quantum graph spectra of a graphyne structure. Zbl 1273.81067
Do, Ngoc T.; Kuchment, Peter
2013
Detecting small low emission radiating sources. Zbl 1266.82083
Allmaras, Moritz; Darrow, David; Hristova, Yulia; Kanschat, Guido; Kuchment, Peter
2013
Identities for $$\sin x$$ that came from medical imaging. Zbl 1278.33001
Kuchment, Peter; Lvin, Sergey
2013
Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths. Zbl 1317.81127
Berkolaiko, G.; Kuchment, P.
2012
Stabilizing inverse problems by internal data. Zbl 1252.92037
Kuchment, Peter; Steinhauer, Dustin
2012
Mathematics of hybrid imaging: A brief review. Zbl 1248.65102
Kuchment, Peter
2012
Critical partitions and nodal deficiency of billiard eigenfunctions. Zbl 1308.35152
Berkolaiko, Gregory; Kuchment, Peter; Smilansky, Uzy
2012
Green’s function asymptotics near the internal edges of spectra of periodic elliptic operators: Spectral edge case. Zbl 1257.35080
Kuchment, Peter; Raich, Andrew
2012
Mathematics of photoacoustic and thermoacoustic tomography. Zbl 1259.92065
Kuchment, Peter; Kunyansky, Leonid
2011
2D and 3D reconstructions in acousto-electric tomography. Zbl 1217.35211
Kuchment, Peter; Kunyansky, Leonid
2011
A Bayesian approach to the detection of small low emission sources. Zbl 1228.62035
Xun, Xiaolei; Mallick, Bani; Carroll, Raymond J.; Kuchment, Peter
2011
The support theorem for the single radius spherical mean transform. Zbl 1254.44001
Agranovsky, M.; Kuchment, P.
2011
Remembering Leon Ehrenpreis (1930–2010). Zbl 1225.01086
Struppa, Daniele C.; Farkas, Hershel; Kawai, Takahiro; Kuchment, Peter; Quinto, Eric Todd; Sternberg, Shlomo; Taylor, Alan
2011
Spectral theory and geometric analysis. International conference in honor of Mikhail Shubin’s 65th birthday, Northeastern University, Boston, MA, USA, July 29 – August 2, 2009. Zbl 1207.58001
Braverman, Maxim (ed.); Friedlander, Leonid (ed.); Kappeler, Thomas (ed.); Kuchment, Peter (ed.); Topalov, Peter (ed.); Weitsman, Jonathan (ed.)
2011
On the location of spectral edges in $$\mathbb Z$$-periodic media. Zbl 1204.81063
Exner, Pavel; Kuchment, Peter; Winn, Brian
2010
Synthetic focusing in ultrasound modulated tomography. Zbl 1286.44002
Kuchment, Peter; Kunyansky, Leonid
2010
On guided electromagnetic waves in photonic crystal waveguides. Zbl 1217.35181
Kuchment, Peter; Ong, Beng-Seong
2010
Range conditions for a spherical mean transform. Zbl 1190.44001
Agranovsky, Mark; Finch, David; Kuchment, Peter
2009
Tight frames of exponentially decaying Wannier functions. Zbl 1154.82028
Kuchment, Peter
2009
Mathematics of thermoacoustic tomography. Zbl 1185.35327
Kuchment, Peter; Kunyansky, Leonid
2008
Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media. Zbl 1180.35563
Hristova, Yulia; Kuchment, Peter; Nguyen, Linh
2008
Analysis on graphs and its applications. Selected papers based on the Isaac Newton Institute for Mathematical Sciences programme, Cambridge, UK, January 8–June 29, 2007. Zbl 1143.05002
Exner, Pavel (ed.); Keating, Jonathan P. (ed.); Kuchment, Peter (ed.); Sunada, Toshikazu (ed.); Teplyaev, Alexander (ed.)
2008
Quantum graphs: an introduction and a brief survey. Zbl 1210.05169
Kuchment, Peter
2008
Vladimir A. Geyler, April 29, 1943–April 2, 2007. Zbl 1190.01017
Exner, Pavel; Keating, Jonathan P.; Kuchment, Peter; Sunada, Toshikazu; Teplyaev, Alexander
2008
On the spectra of carbon nano-structures. Zbl 1145.81032
Kuchment, Peter; Post, Olaf
2007
Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed. Zbl 1126.35087
Agranovsky, Mark; Kuchment, Peter
2007
Index theorems for quantum graphs. Zbl 1127.58027
Fulling, S. A.; Kuchment, P.; Wilson, J. H.
2007
On occurrence of spectral edges for periodic operators inside the Brillouin zone. Zbl 1141.82340
Harrison, Jon M.; Kuchment, P.; Sobolev, A.; Winn, B.
2007
Range descriptions for the spherical mean Radon transform. Zbl 1132.44002
Agranovsky, Mark; Kuchment, Peter; Quinto, Eric Todd
2007
A range description for the planar circular Radon transform. Zbl 1120.44003
Ambartsoumian, Gaik; Kuchment, Peter
2007
Liouville theorems and spectral edge behavior on Abelian coverings of compact manifolds. Zbl 1127.58015
Kuchment, Peter; Pinchover, Yehuda
2007
Integral representations of solutions of periodic elliptic equations. Zbl 1133.35033
Kuchment, Peter
2007
Quantum graphs and their applications. Proceedings of an AMS-IMS-SIAM joint summer research conference on quantum graphs and their applications, Snowbird, UT, USA, June 19–23, 2005. Zbl 1098.81007
Berkolaiko, Gregory (ed.); Carlson, Robert (ed.); Fulling, Stephen A. (ed.); Kuchment, Peter (ed.)
2006
On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators. Zbl 1125.39021
Kuchment, Peter; Vainberg, Boris
2006
Generalized transforms of Radon type and their applications. Zbl 1118.44001
Kuchment, Peter
2006
Quantum graphs. II: Some spectral properties of quantum and combinatorial graphs. Zbl 1070.81062
Kuchment, Peter
2005
On the injectivity of the circular Radon transform. Zbl 1072.44001
Ambartsoumian, Gaik; Kuchment, Peter
2005
Coincidence of length spectra does not imply isospectrality. Zbl 1083.35077
Fulling, S. A.; Kuchment, Peter
2005
Quantum graphs. I: Some basic structures. Zbl 1063.81058
Kuchment, Peter
2004
One some spectral problems of mathematical physics. Zbl 1061.35065
Kuchment, Peter
2004
Special issue: Dedicated to Professor Robert Brooks. Zbl 1076.81500
Kuchment, P. (ed.)
2004
Asymptotics of spectra of Neumann Laplacians in thin domains. Zbl 1050.35094
Kuchment, Peter; Zeng, Honbiao
2003
On guided waves in photonic crystal waveguides. Zbl 1046.35081
Kuchment, Peter; Ong, BengSeong
2003
Differential and pseudo-differential operators on graphs as models of mesoscopic systems. Zbl 1200.82086
Kuchment, Peter
2003
Waves in periodic and random media. Proceedings of an AMS-IMS-SIAM joint summer research conference, South Hadley, MA, USA, June 22–28, 2002. Zbl 1029.00026
Kuchment, Peter (ed.)
2003
Graph models for waves in thin structures. Zbl 1063.35525
Kuchment, Peter
2002
On the structure of spectra of periodic elliptic operators. Zbl 1058.35174
Kuchment, Peter; Levendorskiĭ, Sergei
2002
Differential operators on graphs and photonic crystals. Zbl 0993.65122
Kuchment, P.; Kunyansky, L.
2002
The mathematics of photonic crystals. Zbl 0986.78004
Kuchment, Peter
2001
Convergence of spectra of mesoscopic systems collapsing onto a graph. Zbl 0982.35076
Kuchment, Peter; Zeng, Hongbiao
2001
Integral representations and Liouville theorems for solutions of periodic elliptic equations. Zbl 0986.35028
Kuchment, Peter; Pinchover, Yehuda
2001
On absence of embedded eigenvalues for Schrödinger operators with perturbed periodic potentials. Zbl 0960.35077
Kuchment, Peter; Vainberg, Boris
2000
Numerical harmonic analysis on the hyperbolic plane. Zbl 1022.65145
Fridman, Buma; Kuchment, Peter; Lancaster, Kirk; Lissianoi, Serguei; Mogilevsky, Mila
2000
An efficient finite element method for computing spectra of photonic and acoustic band-gap materials. I: Scalar case. Zbl 0963.78028
Axmann, Waldemar; Kuchment, Peter
1999
Spectral properties of high contrast band-gap materials and operators on graphs. Zbl 0930.35112
Kuchment, Peter; Kunyansky, Leonid A.
1999
Iosif Shneiberg, July 26, 1950 - July 21, 1992. Zbl 0938.01043
Krein, Selim; Kuchment, Peter; Ovchinnikov, Vladimir; Semenov, Evgeny
1999
On absolute continuity of spectra of periodic elliptic operators. Zbl 0965.35100
Kuchment, Peter; Levendorskiǐ, Sergei
1999
Spectral properties of classical waves in high-contrast periodic media. Zbl 0916.35011
Figotin, A.; Kuchment, P.
1998
On embedding eigenvalues of perturbed periodic Schrödinger operators. Zbl 0902.35077
Kuchment, Peter; Vainberg, Boris
1998
Solution of the linearized inverse conductivity problem in a half space via integral geometry. Zbl 0904.35096
Fridman, Buma; Kuchment, Peter; Ma, Daowei; Papanicolaou, Vassilis G.
1998
2D photonic crystals with cubic structure: Asymptotic analysis. Zbl 0901.65078
Figotin, A.; Kuchment, P.
1998
Voronezh winter mathematical schools. Dedicated to Selim Krein. Zbl 0997.00561
Kuchment, Peter (ed.); Lin, Vladimir (ed.)
1998
Band-gap structure of spectra of periodic dielectric and acoustic media. I: Scalar model. Zbl 0852.35014
Figotin, Alex; Kuchment, Peter
1996
Band-gap structure of spectra of periodic dielectric and acoustic media. II: Two-dimensional photonic crystals. Zbl 0868.35009
Figotin, A.; Kuchment, P.
1996
Approximation by spherical waves in $$L^p$$-spaces. Zbl 0898.44003
Agranovsky, Mark; Berenstein, Carlos; Kuchment, Peter
1996
Range conditions for the exponential Radon transform. Zbl 0858.44002
Aguilar, Valentina; Ehrenpreis, Leon; Kuchment, Peter
1996
On local tomography. Zbl 0832.44001
Kuchment, Peter; Lancaster, Kirk; Mogilevskaya, Lyudmila
1995
Range conditions for the multidimensional exponential x-ray transform. Zbl 0843.44005
Aguilar, Valentina; Kuchment, Peter
1995
Some inversion formulas in the single photon emission computed tomography. Zbl 0839.44002
Kuchment, Peter; Shneiberg, Iosiph
1994
Band-gap structure of the spectrum of periodic Maxwell operators. Zbl 0946.82517
Figotin, Alexander; Kuchment, Peter
1994
On inversion and range characterization of one transform arising in emission tomography. Zbl 0823.44007
Kuchment, P.
1994
Tomography, impedance imaging, and integral geometry. 1993 AMS-SIAM summer seminar, June 7-18, 1993, Mount Holyoke College, South Hadley, MA,, USA. Zbl 0801.00052
Quinto, Eric Todd (ed.); Cheney, Margaret (ed.); Kuchment, Peter (ed.)
1994
On the behavior of Floquet exponents of a kind of periodic evolution problems. Zbl 0792.35026
Kuchment, Peter
1994
Floquet theory for partial differential equations. Zbl 0789.35002
Kuchment, Peter
1993
On positivity problems for the Radon transform and some related transforms. Zbl 0785.44003
Kuchment, Peter
1992
On the Floquet theory of periodic difference equations. Zbl 0979.39011
Kuchment, P. A.
1991
Paley-Wiener theorem for exponential Radon transform. Zbl 0705.44001
Kuchment, Peter A.; L’Vin, Sergej Ya.
1990
The range of the exponential Radon transform. Zbl 0748.44002
Kuchment, P. A.; L’vin, S. Ya.
1990
Spherical representation of solutions of invariant differential equations on a symmetric Riemannian space of noncompact type. Zbl 0593.58044
Kuchment, P. A.
1985
Representations of solutions of periodic partial differential equations. Zbl 0529.35009
Kuchment, P. A.
1983
Floquet theory for partial differential equations. Zbl 0519.35003
Kuchment, P. A.
1982
Representations of solutions of invariant differential equations on certain symmetric spaces. Zbl 0497.58025
Kuchment, P. A.
1981
The absence of $$L_ 2-$$solutions for periodic partial differential equations. Zbl 0461.35029
Kuchment, P. A.
1980
Bloch solutions of periodic partial differential equations. Zbl 0459.35028
Kuchment, P. A.
1980
Floquet representation of solutions of linear hypoelliptic systems of partial differential equations. Zbl 0414.35020
Kuchment, P. A.
1979
On the Floquet representation of exponentially increasing solutions of elliptic equations with periodic coefficients. Zbl 0393.35009
Zelenko, L. B.; Kuchment, P. A.
1978
Reconstruction of a continuous representation with respect to a subrepresentation and a factor representation. Zbl 0332.46047
Kuchment, P. A.
1976
Banach bundles and linear operators. Zbl 0335.47017
Zaĭdenberg, M. G.; Kreĭn, S. G.; Kuchment, P. A.; Pankov, A. A.
1975
Banach bundles and linear operators. Zbl 0317.47018
Zaĭdenberg, M. G.; Kreĭn, S. G.; Kuchment, P. A.; Pankov, A. A.
1975
...and 3 more Documents
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#### Cited by 1,349 Authors

 51 Nazarov, Sergeĭ Aleksandrovich 34 Exner, Pavel 30 Kuchment, Peter A. 24 Haltmeier, Markus 22 Kurasov, Pavel B. 20 Pankrashkin, Konstantin 17 Berkolaiko, Gregory 17 Moon, Sunghwan 17 Scherzer, Otmar 15 Rabinovich, Vladimir Samuilovich 14 Post, Olaf 14 Yang, Chuanfu 13 Ammari, Habib M. 12 Bal, Guillaume 12 Band, Ram 12 Bondarenko, Natalia P. 12 Mugnolo, Delio 11 De Nittis, Giuseppe 11 Quinto, Eric Todd 11 Taskinen, Jari 10 Adami, Riccardo 10 Cacciapuoti, Claudio 10 Lotoreichik, Vladimir 10 Weinstein, Michael I. 9 Borisov, Denis Ivanovich 9 Kunyansky, Leonid A. 9 Lenz, Daniel H. 9 Noja, Diego 9 Rubin, Boris 9 Serra, Enrico 8 Bakharev, Fedor L’vovich 8 Dovetta, Simone 8 Rohleder, Jonathan 8 Veselić, Ivan 7 Alberti, Giovanni S. 7 Ambartsoumian, Gaik 7 Cardone, Giuseppe 7 Cherednichenko, Kirill D. 7 Joly, Patrick 7 Korotyaev, Evgeny L. 7 Nguyen Viet Linh 7 Niikuni, Hiroaki 7 Popov, Igor’ Yur’evich 7 Saburova, Natalia 7 Teplyaev, Alexander 7 Uhlmann, Gunther Alberto 7 Weder, Ricardo A. 6 Agranovsky, Mark L. 6 Bolte, Jens 6 Danilov, Leonid Ivanovich 6 Engström, Christian 6 Khrabustovskyi, Andrii 6 Klopp, Frédéric 6 Lipovský, Jiří 6 Monaco, Domenico 6 Nguyen, Linh Viet 6 Pelinovsky, Dmitry Efimovich 6 Roy, Souvik 6 Seifert, Christian 6 Shipman, Stephen P. 6 Tentarelli, Lorenzo 6 Tilli, Paolo 6 Turek, Ondřej 6 Vaĭnberg, Boris Rufimovich 5 Albeverio, Sergio A. 5 Behrndt, Jussi 5 Bergounioux, Maïtine 5 Cornean, Horia D. 5 Drouot, Alexis 5 Elbau, Peter 5 Fefferman, Charles Louis 5 Figotin, Alexander 5 Finco, Domenico 5 Fliss, Sonia 5 Frikel, Jürgen 5 Giani, Stefano 5 Gomi, Kiyonori 5 Howard, Peter 5 Katsevich, Alexander I. 5 Kerner, Joachim 5 Kiselev, Alexander V. 5 Lein, Max 5 Malamud, Mark M. 5 Monard, François 5 Panati, Gianluca 5 Pankov, Alexander A. 5 Ren, Kui 5 Shafarevich, Andreĭ Igorevich 5 Smilansky, Uzy 5 Tamasan, Alexandru 5 Zhang, Chuanzeng 5 Zheng, Hui 4 Angulo Pava, Jaime 4 Banasiak, Jacek 4 Blinova, Irina V. 4 Conca, Carlos 4 Dobson, David C. 4 Felli, Veronica 4 Fillman, Jake 4 Friedlander, Leonid ...and 1,249 more Authors
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#### Cited in 251 Serials

 61 Journal of Mathematical Analysis and Applications 57 Inverse Problems 54 Journal of Mathematical Physics 38 Communications in Mathematical Physics 30 Journal of Differential Equations 29 Annales Henri Poincaré 27 Journal of Functional Analysis 24 Integral Equations and Operator Theory 21 SIAM Journal on Imaging Sciences 19 Transactions of the American Mathematical Society 19 Journal of Mathematical Sciences (New York) 18 SIAM Journal on Mathematical Analysis 17 St. Petersburg Mathematical Journal 16 Letters in Mathematical Physics 15 Journal of Computational Physics 15 Analysis and Mathematical Physics 14 Functional Analysis and its Applications 14 Inverse Problems and Imaging 13 Applicable Analysis 13 Archive for Rational Mechanics and Analysis 13 Reviews in Mathematical Physics 12 Russian Journal of Mathematical Physics 11 Journal d’Analyse Mathématique 11 Proceedings of the American Mathematical Society 11 SIAM Journal on Applied Mathematics 11 Journal of Inverse and Ill-Posed Problems 11 Journal of Physics A: Mathematical and Theoretical 10 Journal of Computational and Applied Mathematics 9 Journal of Statistical Physics 9 Mathematical Notes 9 Mathematische Nachrichten 9 Communications in Partial Differential Equations 9 Calculus of Variations and Partial Differential Equations 9 Doklady Mathematics 9 Complex Analysis and Operator Theory 8 Israel Journal of Mathematics 8 Reports on Mathematical Physics 8 Numerische Mathematik 8 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 7 Mathematical Methods in the Applied Sciences 7 The Journal of Fourier Analysis and Applications 7 Complex Variables and Elliptic Equations 6 Computers & Mathematics with Applications 6 Physics Letters. A 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Advances in Mathematics 6 Annales de l’Institut Fourier 6 European Journal of Applied Mathematics 6 Linear Algebra and its Applications 6 Journal of Mathematical Imaging and Vision 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Inverse Problems in Science and Engineering 5 Journal of Geometry and Physics 5 Duke Mathematical Journal 5 Results in Mathematics 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Engineering Analysis with Boundary Elements 5 Discrete and Continuous Dynamical Systems 5 Mathematical Physics, Analysis and Geometry 5 Journal of Evolution Equations 5 Waves in Random and Complex Media 5 Symmetry 5 Journal of Spectral Theory 4 Theoretical and Mathematical Physics 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Physica D 4 Applied Mathematics Letters 4 Journal of Nonlinear Science 4 Applied and Computational Harmonic Analysis 4 Opuscula Mathematica 4 Communications on Pure and Applied Analysis 4 Multiscale Modeling & Simulation 4 Proceedings of the Steklov Institute of Mathematics 4 Operators and Matrices 3 Computer Methods in Applied Mechanics and Engineering 3 Nonlinearity 3 Russian Mathematical Surveys 3 Arkiv för Matematik 3 Applied Mathematics and Computation 3 Geometriae Dedicata 3 International Journal for Numerical Methods in Engineering 3 Journal of Approximation Theory 3 Journal of Soviet Mathematics 3 Mathematische Annalen 3 Quarterly of Applied Mathematics 3 SIAM Journal on Numerical Analysis 3 Siberian Mathematical Journal 3 Transactions of the Moscow Mathematical Society 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Applied Numerical Mathematics 3 Optimization 3 Journal of Scientific Computing 3 Computational Mathematics and Mathematical Physics 3 Potential Analysis 3 NoDEA. Nonlinear Differential Equations and Applications 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 Fractional Calculus & Applied Analysis 3 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Communications in Contemporary Mathematics 3 Networks and Heterogeneous Media ...and 151 more Serials
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#### Cited in 56 Fields

 597 Partial differential equations (35-XX) 319 Quantum theory (81-XX) 262 Operator theory (47-XX) 187 Ordinary differential equations (34-XX) 156 Numerical analysis (65-XX) 120 Statistical mechanics, structure of matter (82-XX) 120 Biology and other natural sciences (92-XX) 116 Optics, electromagnetic theory (78-XX) 98 Integral transforms, operational calculus (44-XX) 75 Combinatorics (05-XX) 73 Global analysis, analysis on manifolds (58-XX) 56 Functional analysis (46-XX) 56 Mechanics of deformable solids (74-XX) 44 Information and communication theory, circuits (94-XX) 43 Fluid mechanics (76-XX) 41 Calculus of variations and optimal control; optimization (49-XX) 40 Dynamical systems and ergodic theory (37-XX) 31 Differential geometry (53-XX) 21 Probability theory and stochastic processes (60-XX) 20 Integral equations (45-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 16 Difference and functional equations (39-XX) 16 Abstract harmonic analysis (43-XX) 13 Computer science (68-XX) 13 Systems theory; control (93-XX) 12 Potential theory (31-XX) 12 Several complex variables and analytic spaces (32-XX) 11 Measure and integration (28-XX) 10 Algebraic geometry (14-XX) 9 Manifolds and cell complexes (57-XX) 8 $$K$$-theory (19-XX) 8 Group theory and generalizations (20-XX) 8 Approximations and expansions (41-XX) 8 Convex and discrete geometry (52-XX) 8 Operations research, mathematical programming (90-XX) 7 Functions of a complex variable (30-XX) 7 Algebraic topology (55-XX) 6 History and biography (01-XX) 6 Number theory (11-XX) 6 Topological groups, Lie groups (22-XX) 6 Statistics (62-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 General and overarching topics; collections (00-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Associative rings and algebras (16-XX) 5 Real functions (26-XX) 4 Geometry (51-XX) 3 General topology (54-XX) 3 Mechanics of particles and systems (70-XX) 3 Geophysics (86-XX) 2 Nonassociative rings and algebras (17-XX) 2 Special functions (33-XX) 1 Commutative algebra (13-XX) 1 Category theory; homological algebra (18-XX) 1 Sequences, series, summability (40-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)