Edit Profile (opens in new tab) Solomyak, Mikhaĭl Zakharovich Compute Distance To: Compute Author ID: solomyak.mikhail-zakharovich Published as: Solomyak, M. Z.; Solomyak, Michael; Solomyak, M. more...less External Links: MGP · Math-Net.Ru Documents Indexed: 173 Publications since 1953, including 3 Books 1 Contribution as Editor Biographic References: 3 Publications Co-Authors: 53 Co-Authors with 131 Joint Publications 1,881 Co-Co-Authors all top 5 Co-Authors 41 single-authored 76 Birman, Mikhail Shlëmovich 9 Rozenblum, Grigori V. 6 Naimark, Katherine 6 Yafaev, Dimitri R. 5 Buslaev, Vladimir Savel’evich 5 Laptev, Ari 4 Vershik, Anatoliĭ Moiseevich 4 Vulis, I. L. 3 Friedlander, Leonid 3 Rozenblyum, G. V. 3 Suslina, Tat’yana Aleksandrovna 2 Babich, Vasiliĭ Mikhaĭlovich 2 Evans, William Desmond 2 Faddeev, Lyudvig Dmitrievich 2 Gindikin, Simon Grigorevich 2 Karazeeva, N. A. 2 Matsaev, Vladimir Igorevich 2 Shubin, Mikhail Aleksandrovich 2 Ural’tseva, Nina Nikolaevna 1 Aleksandrov, Aleksandr Danilovich 1 Cezus, Frank A. 1 Gel’fand, Israil’ Moiseevich 1 Khavin, Viktor Petrovich 1 Karadzhov, Georgi Eremiev 1 Kislyakov, Sergeĭ Vital’evich 1 Koplienko, L. S. 1 Kostometov, G. P. 1 Kresin, Gershon I. 1 Kruglov, A. A. 1 Kutateladze, Semën Samsonovich 1 Ladyzhenskaya, Ol’ga Aleksandrovna 1 Leifman, Lev J. 1 Levin, Daniel 1 Marchenko, Vladimir Aleksandrovich 1 Merzbach, Ely 1 Moroz, Vitaly 1 Naboko, Serguei N. 1 Newman, Joshua 1 Nikol’skiĭ, Nikolaĭ Kapitonovich 1 Olevskii, Victor 1 Pastur, Leonid Andreevich 1 Plamenevskiĭ, Boris Alekseevich 1 Prössdorf, Siegfried 1 Reshetnyak, Yuriĭ Grigor’evich 1 Rubinshteĭn, Gennadiĭ Shlemovich 1 Sajon, Ulare 1 Shaposhnikova, Tatyana Olegovna 1 Smilansky, Uzy 1 Smirnov, Vladimir Ivanovich 1 Sobolev, Alexander V. 1 Sobolevskii, Pavel Evseyevich 1 Sten’kin, V. V. 1 Tikhomirov, Vladimir Mikhaĭlovich 1 Truman, Aubrey 1 Verbitsky, E. all top 5 Serials 16 Vestnik Leningradskogo Universiteta. Matematika, Mekhanika, Astronomiya 9 Soviet Mathematics. Doklady 7 Journal of Soviet Mathematics 6 Functional Analysis and its Applications 6 St. Petersburg Mathematical Journal 6 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 5 Izvestiya Vysshikh Uchebnykh Zavedeniĭ, Matematika 5 Russian Mathematical Surveys 5 Integral Equations and Operator Theory 5 Vestnik Leningrad University. Mathematics 3 Matematicheskiĭ Sbornik. Novaya Seriya 3 Proceedings of the London Mathematical Society. Third Series 3 Journal of Physics A: Mathematical and General 3 Journal of Mathematical Sciences (New York) 2 Doklady Akademii Nauk SSSR 2 Israel Journal of Mathematics 2 Journal d’Analyse Mathématique 2 Uspekhi Matematicheskikh Nauk [N. S.] 2 Waves in Random Media 2 Mathematische Nachrichten 2 Mathematics of the USSR. Izvestiya 2 Siberian Mathematical Journal 2 Transactions of the Moscow Mathematical Society 2 Trudy Moskovskogo Matematicheskogo Obshchestva 2 Selecta Mathematica Sovietica 2 Mathematics of the USSR, Sbornik 2 Russian Journal of Mathematical Physics 2 Problemy Matematicheskoĭ Fiziki 2 Translations. Series 2. American Mathematical Society 2 Journal of Spectral Theory 2 Translations. Series 2. American Mathematical Society 1 Communications in Mathematical Physics 1 Mathematical Notes 1 Matematicheskie Zametki 1 Arkiv för Matematik 1 Reviews in Mathematical Physics 1 Bulletin of the London Mathematical Society 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Journal of Approximation Theory 1 Journal of Computational and Applied Mathematics 1 Journal of Functional Analysis 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Sibirskiĭ Matematicheskiĭ Zhurnal 1 Leningrad Mathematical Journal 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Linear Algebra and its Applications 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Journées Équations aux Dérivées Partielles (Saint-Jean-de-Monts) 1 Mathematical Research Letters 1 Problemy Matematicheskogo Analiza 1 Functional Differential Equations 1 Doklady Akademii Nauk SSSR. Novaya Seriya 1 Mathematics and Its Applications. Soviet Series 1 Teoriya Operatorov i Teoriya Funktsiĭ all top 5 Fields 97 Partial differential equations (35-XX) 90 Operator theory (47-XX) 20 Functional analysis (46-XX) 15 Ordinary differential equations (34-XX) 12 History and biography (01-XX) 10 Quantum theory (81-XX) 8 Measure and integration (28-XX) 5 Real functions (26-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Optics, electromagnetic theory (78-XX) 4 Integral equations (45-XX) 3 Combinatorics (05-XX) 2 Potential theory (31-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Probability theory and stochastic processes (60-XX) 2 Fluid mechanics (76-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 151 Publications have been cited 1,873 times in 1,125 Documents Cited by ▼ Year ▼ Spectral theory of self-adjoint operators in Hilbert space. Translation from the 1980 Russian original by S. Khrushchëv and V. Peller. (Спектральная теория самосопряженных операторов в гильбертовом пространстве.) Zbl 0744.47017Birman, M. S.; Solomyak, M. Z. 149 1987 \(L_ 2\)-theory of the Maxwell operator in arbitrary domains. Zbl 0653.35075Birman, M. Sh.; Solomyak, M. Z. 96 1987 Piecewise-polynomial approximations of functions of the class \(W_p^\alpha\). Zbl 0173.16001Birman, M. Sh.; Solomyak, M. Z. 92 1967 Double operator integrals in a Hilbert space. Zbl 1054.47030Birman, Mikhail Sh.; Solomyak, Michael 66 2003 Double Stieltjes operator integrals. II. Zbl 0182.46202Birman, M. Sh.; Solomyak, M. Z. 60 1967 Quantitative analysis in Sobolev imbedding theorems and applications to spectral theory. Transl. from the Russian by F. A. Cezus. Ed. by Lev J. Leifman. Zbl 0426.46020Birman, M. Sh.; Solomyak, M. Z. 50 1980 Double Stieltjes operator integrals. Zbl 0161.34602Birman, M. Sh.; Solomyak, M. Z. 48 1966 Estimates for the singular values of integral operators. Zbl 0344.47021Birman, M. Sh.; Solomyak, M. Z. 47 1977 On the spectrum of the Dirichlet Laplacian in a narrow strip. Zbl 1173.35090Friedlander, Leonid; Solomyak, Michael 45 2009 On a spectral problem related to self-similar measures. Zbl 0823.34071Solomyak, M.; Verbitsky, E. 35 1995 Estimates for the number of negative eigenvalues of the Schrödinger operator and its generalization. Zbl 0749.35026Birman, M. Sh.; Solomyak, M. Z. 32 1991 Eigenvalue estimates for the weighted Laplacian on metric trees. Zbl 1046.34092Naimark, K.; Solomyak, M. 32 2000 Asymptotic behavior of the spectrum of pseudodifferential operators with anisotropically homogeneous symbols. Zbl 0377.47033Birman, M. Sh.; Solomyak, M. Z. 31 1977 Double Stieltjes operator integrals. III: Limit under the integral sign. Zbl 0281.47013Birman, M. Sh.; Solomyak, M. Z. 30 1973 Estimates of singular numbers of integral operators. Zbl 0376.47023Birman, M. Sh.; Solomyak, M. Z. 30 1977 Piecewise-polynomial approximation of functions from \(H^ \ell((0,1)^ d)\), \(2\ell=d\), and applications to the spectral theory of the Schrödinger operator. Zbl 0803.47045Solomyak, M. 29 1994 On the spectrum of narrow periodic waveguides. Zbl 1180.35392Friedlander, L.; Solomyak, M. 27 2008 On the spectrum of the Laplacian on regular metric trees. Zbl 1077.47513Solomyak, Michael 27 2004 Spectral asymptotics of nonsmooth elliptic operators. I. Zbl 0251.35075Birman, M. Sh.; Solomyak, M. Z. 27 1972 Estimates of the spectrum of a difference of fractional powers of selfadjoint operators. Zbl 0313.47020Birman, M. Sh.; Koplienko, L. S.; Solomyak, M. Z. 26 1975 Remarks on the spectral shift function. Zbl 0329.47009Birman, M. Sh.; Solomyak, M. Z. 24 1972 Remarks on the spectral shift function. Zbl 0336.47017Birman, M. Sh.; Solomyak, M. Z. 24 1975 Schrödinger operators on homogeneous metric trees: spectrum in gaps. Zbl 1038.81023Sobolev, Alexander V.; Solomyak, Michael 24 2002 Boundedness conditions and spectrum estimates for the operators \(b (X) a (D)\) and their analogs. Zbl 0768.47025Birman, M. Sh.; Karadzhov, G. E.; Solomyak, M. Z. 23 1991 Asymptotic behavior of the spectrum of differential equations. Zbl 0424.35069Birman, M. Sh.; Solomyak, M. Z. 23 1979 Schrödinger operator. Estimates for number of bound states as function- theoretical problem. Zbl 0756.35057Birman, M. S.; Solomyak, M. Z. 22 1992 The Rozenblum-Lieb-Cwikel inequality for Markov generators. Zbl 0910.47017Levin, Daniel; Solomyak, Michael 22 1997 On the spectrum of the Dirichlet Laplacian in a narrow infinite strip. Zbl 1170.35487Friedlander, Leonid; Solomyak, Michael 21 2008 The application of the semigroup theory to the study of differential equations in Banach spaces. Zbl 0090.09902Solomyak, M. Z. 21 1958 Operator integration, perturbations and commutators. Zbl 0709.47022Birman, M. Sh.; Solomyak, M. Z. 18 1989 The eigenvalue behaviour for the boundary value problems related to self- similar measures on \(\mathbb{R}^ d\). Zbl 0836.60016Naimark, K.; Solomyak, M. 17 1995 Tensor product of a finite number of spectral measures is always a spectral measure. Zbl 0844.47013Birman, M.; Solomyak, M. 16 1996 A remark on the Hardy inequalities. Zbl 0812.26007Solomyak, Michael 16 1994 Two-sided estimates on singular values for a class of integral operators on the semi-axis. Zbl 0817.47024Newman, Joshua; Solomyak, Michael 16 1994 Spectral theory of differential operators. Zbl 0805.35081Rozenblyum, G. V.; Shubin, M. A.; Solomyak, M. Z. 16 1989 Asymptotic behavior of the spectrum of weakly polar integral operators. Zbl 0261.47027Birman, M. Sh.; Solomyak, M. Z. 16 1971 Asymptotics of the spectrum of variational problems on solutions of elliptic equations. Zbl 0427.35050Birman, M. Sh.; Solomyak, M. Z. 15 1979 The asymptotics of the spectrum of pseudo-differential operators with anisotropic-homogeneous symbols. II. Zbl 0439.47040Birman, M. Sh.; Solomyak, M. Z. 15 1979 Spectral theory of differential operators. Zbl 0715.35057Rozenblyum, G. V.; Solomyak, M. Z.; Shubin, M. A. 15 1989 The self-adjoint Maxwell operator in arbitrary domains. Zbl 0733.35099Birman, M. Sh.; Solomyak, M. Z. 15 1990 On approximation of functions from Sobolev spaces on metric graphs. Zbl 1027.46037Solomyak, Michael 15 2003 Geometry of Sobolev spaces on regular trees and the Hardy inequalities. Zbl 1187.46028Naimark, K.; Solomyak, M. 14 2001 On the spectral estimates for the Schrödinger operator on \(\mathbb Z^d\), \(d \geqslant 3\). Zbl 1207.35237Rozenblum, Grigori; Solomyak, Michael 14 2009 Maxwell operator in regions with nonsmooth boundaries. Zbl 0655.35067Birman, M. Sh.; Solomyak, M. Z. 13 1987 The Weyl asymptotics of the spectrum of the Maxwell operator for domains with a Lipschitz boundary. Zbl 0639.35062Birman, M. Sh.; Solomyak, M. Z. 12 1987 On subspaces admitting a pseudodifferential projector. Zbl 0484.35085Birman, M. Sh.; Solomyak, M. Z. 11 1982 Counting Schrödinger boundstates: Semiclassics and beyond. Zbl 1172.35046Rozenblum, Grigori; Solomyak, Michael 11 2009 Leading term in the asymptotic spectral formula for ”nonsmooth” elliptic problems. Zbl 0225.35077Birman, M. Sh.; Solomyak, M. Z. 11 1970 On the negative spectrum of the two-dimensional Schrödinger operator with radial potential. Zbl 1253.35037Laptev, A.; Solomyak, M. 11 2012 On the negative discrete spectrum of a periodic elliptic operator in a waveguide-type domain, perturbed by a decaying potential. Zbl 1200.35196Birman, M. Sh.; Solomyak, M. 10 2001 Regular and pathological eigenvalue behavior for the equation \(-\lambda u''=Vu\) on the semiaxis. Zbl 0895.34063Naimark, K.; Solomyak, M. 10 1997 On eigenvalue estimates for the weighted Laplacian on metric graphs. Zbl 1045.35048Solomyak, Michael 10 2002 On spectral estimates for two-dimensional Schrödinger operators. Zbl 1294.35048Laptev, Ari; Solomyak, Michael 10 2013 Evaluation of the norm of the resolvent of an elliptic operator in \(L_p\)-spaces. (Abschätzung der Norm der Resolvente eines elliptischen Operators in \(L_p\)-Räumen.) Zbl 0102.31501Solomyak, M. Z. 9 1960 Product of commuting spectral measures need not be countably additive. Zbl 0423.28008Birman, M. Sh.; Vershik, A. M.; Solomyak, M. Z. 9 1979 Quantitative analysis in Sobolev imbedding theorems and applications to spectral theory. Tenth Mathematical School (Summer School, Katsiveli/Nalchik, 1972). (Количественный анализ в теоремах вложения Соболева и приложения к спектральной теории. (Десятая Математическая Школа.) Zbl 0426.46019Birman, M. Sh.; Solomyak, M. Z. 9 1974 The negative discrete spectrum of the operator \((-\Delta)^ l-\alpha V\) in \(L_ 2(\mathbb{R}^ d)\) for \(d\) even and \(2l\geq d\). Zbl 0876.35079Birman, Mikhail Sh.; Laptev, Ari; Solomyak, Michael 9 1997 On principal eigenvalues for indefinite problems in Euclidean space. Zbl 0908.35085Rozenblum, Grigori; Solomyak, Michael 9 1998 On the eigenvalue behaviour for a class of differential operators on the semiaxis. Zbl 0916.34067Birman, M. Sh.; Laptev, A.; Solomyak, M. 9 1998 Smilansky’s model of irreversible quantum graphs. I: The absolutely continuous spectrum. Zbl 1064.81037Evans, W. D.; Solomyak, M. 9 2005 The analytic nature of the semigroup generated by an elliptic operator in \(L_p\) spaces. Zbl 0087.11703Solomyak, M. Z. 9 1959 Spectral asymptotics of degenerate elliptic operators. Zbl 0268.35070Vulis, I. L.; Solomyak, M. Z. 8 1972 Spectral asymptotics of nonsmooth elliptic operators. II. Zbl 0281.35079Birman, M. Sh.; Solomyak, M. Z. 8 1973 On the absolutely continuous spectrum in a model of an irreversible quantum graph. Zbl 1098.81036Naboko, Sergey N.; Solomyak, Michael 8 2006 On spectral estimates for Schrödinger-type operators: the case of small local dimension. Zbl 1272.47055Rozenblum, G. V.; Solomyak, M. Z. 8 2010 Asymptotics of the spectrum of variational problems on solutions of elliptic equations in unbounded domains. Zbl 0463.35061Birman, M. Sh.; Solomyak, M. Z. 7 1981 Spectral problems related to the critical exponent in the Sobolev embedding theorem. Zbl 0831.35116Solomyak, M. 7 1995 On the main singularities of the electric component of the electro- magnetic field in regions with screens. Zbl 0804.35127Birman, M. Sh.; Solomyak, M. Z. 7 1993 Asymptotics of the spectrum of the Schrödinger operator with nonregular homogeneous potential. Zbl 0657.35099Solomyak, M. Z. 7 1986 On the asymptotic spectrum of ”nonsmooth” elliptic equations. Zbl 0226.35072Birman, M. Sh.; Solomyak, M. Z. 7 1971 Estimates of singular values of integral operators. III: Operators in unbounded domains. Zbl 0181.13601Birman, M. Sh.; Solomyak, M. Z. 7 1969 Spectral estimates for Schrödinger operators with sparse potentials on graphs. Zbl 1290.35284Rozenblum, G.; Solomyak, M. 6 2011 On the discrete spectrum of a family of differential operators. Zbl 1084.47038Solomyak, M. Z. 6 2004 Smilansky’s model of irreversible quantum graphs. II: The point spectrum. Zbl 1083.81519Evans, W. D.; Solomyak, M. 6 2005 On the eigenvalue behaviour for a class of operators related to self- similar measures on \(\mathbb{R}^ d\). Zbl 0808.60038Naimark, Katherine; Solomyak, Michael 6 1994 Construction in a piecewise smooth domain of a function of the class \(H^ 2\) from the value of the conormal derivative. Zbl 0696.46039Birman, M. Sh.; Solomyak, M. Z. 6 1990 The quantum graph as a limit of a network of physical wires. Zbl 1119.34026Smilansky, Uzy; Solomyak, Michael 5 2006 Equivalent renormings of \(W_p^r\) classes in the case of partitioning of the domain. Zbl 0269.46024Birman, M. Sh.; Solomyak, M. Z. 5 1973 On a family of differential operators with the coupling parameter in the boundary condition. Zbl 1146.35064Rozenblum, G.; Solomyak, M. 5 2007 On the limiting behaviour of the spectra of a family of differential operators. Zbl 1105.35064Solomyak, Michael 5 2006 On a mathematical model of irreversible quantum graphs. Zbl 1264.47051Solomyak, M. Z. 5 2006 Estimates of difference of fractional powers of selfadjoint operators in case of unbounded perturbations. Zbl 0709.47004Birman, M. Sh.; Solomyak, M. Z. 5 1989 Compact operators with the power asymptotics of singular numbers. Zbl 0518.47014Birman, M. Sh.; Solomyak, M. Z. 5 1983 Asymptotics of the spectrum of pseudodifferential variational problems with restrictions. Zbl 0602.35086Birman, M. S.; Solomyak, M. Z. 5 1986 CLR-estimate revisited: Lieb’s approach with no path integrals. Zbl 1027.47020Rozenblum, G.; Solomyak, M. 5 1997 Laplace and Schrödinger operators on regular metric trees: The discrete spectrum case. Zbl 1079.34065Solomyak, Michael 5 2003 Linear elliptic systems of the firs order. Zbl 0163.34602Solomyak, M. Z. 5 1963 Spectral asymptotics of nonsmooth elliptic operators. Zbl 0264.35056Birman, M. Sh.; Solomyak, M. Z. 4 1972 Eigenvalue estimates for a class of operators related to self-similar measures. Zbl 0881.58072Solomyak, Michael 4 1994 CLR-estimate for the generators of positivity preserving and positively dominated semi-groups. Zbl 0911.47025Rozenblyum, G.; Solomyak, M. 4 1997 An estimate for Schur multipliers in \(S_ p\)-classes. Zbl 0806.15020Olevskii, V.; Solomyak, M. 4 1994 Estimates of singular values of integral operators. II. Zbl 0177.18802Birman, M. Sh.; Solomyak, M. Z. 4 1967 Remarks on the nuclearity of integral operators and the boundedness of pseudodifferential operators. Zbl 0187.08501Birman, M. Sh.; Solomyak, M. Z. 4 1969 Asymptotics of the spectrum of the Schrödinger operator with a nonregular homogeneous potential. Zbl 0583.35083Solomyak, M. Z. 4 1985 Negative discrete spectrum of the Schrödinger operator with large coupling constant: A qualitative discussion. Zbl 0746.35024Birman, M. S.; Solomyak, M. Z. 3 1990 The asymptotics of the spectrum of the contact problem for second order elliptic equations. Zbl 0484.35065Karazeeva, N. A.; Solomyak, M. Z. 3 1981 Asymptotics of the spectrum of variational problems on solutions of elliptic systems. Zbl 0501.35065Birman, M. Sh.; Solomyak, M. Z. 3 1982 Spectral asymptotics of nonsmooth elliptic operators. II. Zbl 0296.35066Birman, M. Sh.; Solomyak, M. Z. 3 1975 On a class of spectral problems on the half-line and their applications to multi-dimensional problems. Zbl 1270.34197Solomyak, Michael 3 2013 On the number of negative eigenvalues for the two-dimensional magnetic Schrödinger operator. Zbl 0920.35101Rozenblum, G.; Solomyak, M. 3 1999 On spectral estimates for two-dimensional Schrödinger operators. Zbl 1294.35048Laptev, Ari; Solomyak, Michael 10 2013 On a class of spectral problems on the half-line and their applications to multi-dimensional problems. Zbl 1270.34197Solomyak, Michael 3 2013 On the negative spectrum of the two-dimensional Schrödinger operator with radial potential. Zbl 1253.35037Laptev, A.; Solomyak, M. 11 2012 On the mathematical work of M. Sh. Birman. Zbl 1236.01029Solomyak, M. Z.; Suslina, T. A.; Yafaev, D. R. 1 2012 Spectral estimates for Schrödinger operators with sparse potentials on graphs. Zbl 1290.35284Rozenblum, G.; Solomyak, M. 6 2011 On spectral estimates for Schrödinger-type operators: the case of small local dimension. Zbl 1272.47055Rozenblum, G. V.; Solomyak, M. Z. 8 2010 Mikhail Shlemovich Birman (obituary). Zbl 1219.01025Babich, V. M.; Buslaev, V. S.; Vershik, A. M.; Gindikin, S. G.; Kislyakov, S. V.; Laptev, A.; Marchenko, V. A.; Nikol’skii, N. K.; Pastur, L. A.; Plamenevskii, B. A.; Solomyak, M. Z.; Suslina, T. A.; Ural’tseva, N. N.; Faddeev, L. D.; Khavin, V. P.; Yafaev, D. R. 1 2010 On the spectrum of the Dirichlet Laplacian in a narrow strip. Zbl 1173.35090Friedlander, Leonid; Solomyak, Michael 45 2009 On the spectral estimates for the Schrödinger operator on \(\mathbb Z^d\), \(d \geqslant 3\). Zbl 1207.35237Rozenblum, Grigori; Solomyak, Michael 14 2009 Counting Schrödinger boundstates: Semiclassics and beyond. Zbl 1172.35046Rozenblum, Grigori; Solomyak, Michael 11 2009 Remarks on counting negative eigenvalues of the Schrödinger operator on regular metric trees. Zbl 1196.34037Solomyak, Michael 2 2009 On the spectrum of narrow periodic waveguides. Zbl 1180.35392Friedlander, L.; Solomyak, M. 27 2008 On the spectrum of the Dirichlet Laplacian in a narrow infinite strip. Zbl 1170.35487Friedlander, Leonid; Solomyak, Michael 21 2008 On the scientific work of M. Sh. Birman in 1998–2007. Continuation of the list of publications of M. Sh. Birman. Zbl 1159.01011Solomyak, M.; Suslina, T. 2 2008 On a family of differential operators with the coupling parameter in the boundary condition. Zbl 1146.35064Rozenblum, G.; Solomyak, M. 5 2007 On the absolutely continuous spectrum in a model of an irreversible quantum graph. Zbl 1098.81036Naboko, Sergey N.; Solomyak, Michael 8 2006 The quantum graph as a limit of a network of physical wires. Zbl 1119.34026Smilansky, Uzy; Solomyak, Michael 5 2006 On the limiting behaviour of the spectra of a family of differential operators. Zbl 1105.35064Solomyak, Michael 5 2006 On a mathematical model of irreversible quantum graphs. Zbl 1264.47051Solomyak, M. Z. 5 2006 Smilansky’s model of irreversible quantum graphs. I: The absolutely continuous spectrum. Zbl 1064.81037Evans, W. D.; Solomyak, M. 9 2005 Smilansky’s model of irreversible quantum graphs. II: The point spectrum. Zbl 1083.81519Evans, W. D.; Solomyak, M. 6 2005 On the spectrum of the Laplacian on regular metric trees. Zbl 1077.47513Solomyak, Michael 27 2004 On the discrete spectrum of a family of differential operators. Zbl 1084.47038Solomyak, M. Z. 6 2004 On a differential operator appearing in the theory of irreversible quantum graphs. Zbl 1063.35124Solomyak, Michael 3 2004 Mikhail Shlemovich Birman (on the occasion of his 75th birthday). Zbl 1061.01500Buslaev, V. S.; Solomyak, M. Z.; Yafaev, D. R. 1 2004 Double operator integrals in a Hilbert space. Zbl 1054.47030Birman, Mikhail Sh.; Solomyak, Michael 66 2003 On approximation of functions from Sobolev spaces on metric graphs. Zbl 1027.46037Solomyak, Michael 15 2003 Laplace and Schrödinger operators on regular metric trees: The discrete spectrum case. Zbl 1079.34065Solomyak, Michael 5 2003 Schrödinger operators on homogeneous metric trees: spectrum in gaps. Zbl 1038.81023Sobolev, Alexander V.; Solomyak, Michael 24 2002 On eigenvalue estimates for the weighted Laplacian on metric graphs. Zbl 1045.35048Solomyak, Michael 10 2002 Geometry of Sobolev spaces on regular trees and the Hardy inequalities. Zbl 1187.46028Naimark, K.; Solomyak, M. 14 2001 On the negative discrete spectrum of a periodic elliptic operator in a waveguide-type domain, perturbed by a decaying potential. Zbl 1200.35196Birman, M. Sh.; Solomyak, M. 10 2001 Eigenvalue distribution of some fractal semi-elliptic differential operators: Combinatorial approach. Zbl 0983.35096Naimark, K.; Solomyak, M. 3 2001 A few words about V. A. Zalgaller. Zbl 1077.01533Solomyak, M. Z. 1 2001 Eigenvalue estimates for the weighted Laplacian on metric trees. Zbl 1046.34092Naimark, K.; Solomyak, M. 32 2000 Estimates for the approximation numbers of the weighted Riemann-Liouville operator in the spaces \(L_p\). Zbl 0976.47028Solomyak, Michael 2 2000 Mikhail Shlyomovich Birman (on his 70th birthday). Zbl 0958.01026Buslaev, V. S.; Vershik, A. M.; Gel’fand, I. M.; Gindikin, S. G.; Ladyzhenskaya, O. A.; Solomyak, M. Z.; Faddeev, L. D.; Yafaev, D. R. 2 2000 On the number of negative eigenvalues for the two-dimensional magnetic Schrödinger operator. Zbl 0920.35101Rozenblum, G.; Solomyak, M. 3 1999 On the scientific work of Mikhail Shlëmovich Birman. List of publications of M. Sh. Birman. Zbl 1026.01503Buslaev, V.; Solomyak, M.; Yafaev, D. 2 1999 Differential operators and spectral theory. M. Sh. Birman’s 70th anniversary collection. Zbl 0911.00011 1 1999 On principal eigenvalues for indefinite problems in Euclidean space. Zbl 0908.35085Rozenblum, Grigori; Solomyak, Michael 9 1998 On the eigenvalue behaviour for a class of differential operators on the semiaxis. Zbl 0916.34067Birman, M. Sh.; Laptev, A.; Solomyak, M. 9 1998 On the discrete spectrum of a class of problems involving the Neumann Laplacian in unbounded domains. Zbl 0906.35065Solomyak, Michael 2 1998 The Rozenblum-Lieb-Cwikel inequality for Markov generators. Zbl 0910.47017Levin, Daniel; Solomyak, Michael 22 1997 Regular and pathological eigenvalue behavior for the equation \(-\lambda u''=Vu\) on the semiaxis. Zbl 0895.34063Naimark, K.; Solomyak, M. 10 1997 The negative discrete spectrum of the operator \((-\Delta)^ l-\alpha V\) in \(L_ 2(\mathbb{R}^ d)\) for \(d\) even and \(2l\geq d\). Zbl 0876.35079Birman, Mikhail Sh.; Laptev, Ari; Solomyak, Michael 9 1997 CLR-estimate revisited: Lieb’s approach with no path integrals. Zbl 1027.47020Rozenblum, G.; Solomyak, M. 5 1997 CLR-estimate for the generators of positivity preserving and positively dominated semi-groups. Zbl 0911.47025Rozenblyum, G.; Solomyak, M. 4 1997 On the negative discrete spectrum of the operator \(-\Delta_ N-\alpha V\) for a class of unbounded domains in \(\mathbb{R}^ d\). Zbl 0888.35075Solomyak, Michael 1 1997 Tensor product of a finite number of spectral measures is always a spectral measure. Zbl 0844.47013Birman, M.; Solomyak, M. 16 1996 On a spectral problem related to self-similar measures. Zbl 0823.34071Solomyak, M.; Verbitsky, E. 35 1995 The eigenvalue behaviour for the boundary value problems related to self- similar measures on \(\mathbb{R}^ d\). Zbl 0836.60016Naimark, K.; Solomyak, M. 17 1995 Spectral problems related to the critical exponent in the Sobolev embedding theorem. Zbl 0831.35116Solomyak, M. 7 1995 Piecewise-polynomial approximation of functions from \(H^ \ell((0,1)^ d)\), \(2\ell=d\), and applications to the spectral theory of the Schrödinger operator. Zbl 0803.47045Solomyak, M. 29 1994 A remark on the Hardy inequalities. Zbl 0812.26007Solomyak, Michael 16 1994 Two-sided estimates on singular values for a class of integral operators on the semi-axis. Zbl 0817.47024Newman, Joshua; Solomyak, Michael 16 1994 On the eigenvalue behaviour for a class of operators related to self- similar measures on \(\mathbb{R}^ d\). Zbl 0808.60038Naimark, Katherine; Solomyak, Michael 6 1994 Eigenvalue estimates for a class of operators related to self-similar measures. Zbl 0881.58072Solomyak, Michael 4 1994 An estimate for Schur multipliers in \(S_ p\)-classes. Zbl 0806.15020Olevskii, V.; Solomyak, M. 4 1994 My recollections of Ilya Bakelman. Zbl 0879.01031Solomyak, Michael 1 1994 On the main singularities of the electric component of the electro- magnetic field in regions with screens. Zbl 0804.35127Birman, M. Sh.; Solomyak, M. Z. 7 1993 Schrödinger operator. Estimates for number of bound states as function- theoretical problem. Zbl 0756.35057Birman, M. S.; Solomyak, M. Z. 22 1992 On simultaneous action of Markov shift and adic transformation. Zbl 0771.28014Solomyak, M. 2 1992 Estimates for the number of negative eigenvalues of the Schrödinger operator and its generalization. Zbl 0749.35026Birman, M. Sh.; Solomyak, M. Z. 32 1991 Boundedness conditions and spectrum estimates for the operators \(b (X) a (D)\) and their analogs. Zbl 0768.47025Birman, M. Sh.; Karadzhov, G. E.; Solomyak, M. Z. 23 1991 Viktor Abramovich Zalgaller (on his seventieth birthday). Zbl 0744.01010Aleksandrov, A. D.; Kutateladze, S. S.; Reshetnyak, Yu. G.; Rubinshteĭn, G. Sh.; Solomyak, M. Z. 2 1991 The estimates for the number of negative bound states of the Schrödinger operator for large coupling constants. Zbl 0748.35021Birman, M. S.; Solomyak, M. Z. 1 1991 The self-adjoint Maxwell operator in arbitrary domains. Zbl 0733.35099Birman, M. Sh.; Solomyak, M. Z. 15 1990 Construction in a piecewise smooth domain of a function of the class \(H^ 2\) from the value of the conormal derivative. Zbl 0696.46039Birman, M. Sh.; Solomyak, M. Z. 6 1990 Negative discrete spectrum of the Schrödinger operator with large coupling constant: A qualitative discussion. Zbl 0746.35024Birman, M. S.; Solomyak, M. Z. 3 1990 Operator integration, perturbations and commutators. Zbl 0709.47022Birman, M. Sh.; Solomyak, M. Z. 18 1989 Spectral theory of differential operators. Zbl 0805.35081Rozenblyum, G. V.; Shubin, M. A.; Solomyak, M. Z. 16 1989 Spectral theory of differential operators. Zbl 0715.35057Rozenblyum, G. V.; Solomyak, M. Z.; Shubin, M. A. 15 1989 Estimates of difference of fractional powers of selfadjoint operators in case of unbounded perturbations. Zbl 0709.47004Birman, M. Sh.; Solomyak, M. Z. 5 1989 Estimates for the difference of fractional powers of selfadjoint operators in the case of unbounded perturbations. Zbl 0784.47011Birman, M. Sh.; Solomyak, M. Z. 3 1989 Operator integration, perturbations, and commutators. Zbl 0784.47033Birman, M. Sh.; Solomyak, M. Z. 2 1989 Spectral theory of self-adjoint operators in Hilbert space. Translation from the 1980 Russian original by S. Khrushchëv and V. Peller. (Спектральная теория самосопряженных операторов в гильбертовом пространстве.) Zbl 0744.47017Birman, M. S.; Solomyak, M. Z. 149 1987 \(L_ 2\)-theory of the Maxwell operator in arbitrary domains. Zbl 0653.35075Birman, M. Sh.; Solomyak, M. Z. 96 1987 Maxwell operator in regions with nonsmooth boundaries. Zbl 0655.35067Birman, M. Sh.; Solomyak, M. Z. 13 1987 The Weyl asymptotics of the spectrum of the Maxwell operator for domains with a Lipschitz boundary. Zbl 0639.35062Birman, M. Sh.; Solomyak, M. Z. 12 1987 Construction of a function of class \(H^ 2\) with given conormal derivative in a piecewise smooth domain. Zbl 0677.46042Birman, M. Sh.; Solomyak, M. Z. 2 1987 Asymptotics of the spectrum of the Schrödinger operator with nonregular homogeneous potential. Zbl 0657.35099Solomyak, M. Z. 7 1986 Asymptotics of the spectrum of pseudodifferential variational problems with restrictions. Zbl 0602.35086Birman, M. S.; Solomyak, M. Z. 5 1986 Asymptotics of the spectrum of the Schrödinger operator with a nonregular homogeneous potential. Zbl 0583.35083Solomyak, M. Z. 4 1985 Asymptotic behavior of the spectrum of variational problems on the solutions of elliptic systems. Zbl 0562.35064Birman, M. Sh.; Solomyak, M. Z. 1 1985 Application of interpolation methods to estimates of the spectrum of integral operators. Zbl 0606.46047Birman, M. Sh.; Solomyak, M. Z. 1 1985 On the asymptotics of the spectrum of the Schrödinger operator with a nonregular operator with a nonregular homogeneous potential. Zbl 0588.35069Solomyak, M. Z. 2 1984 Compact operators whose singular numbers have powerlike asymptotics. Zbl 0546.47010Birman, M. Sh.; Solomyak, M. Z. 1 1984 Compact operators with the power asymptotics of singular numbers. Zbl 0518.47014Birman, M. Sh.; Solomyak, M. Z. 5 1983 On the Calderon projector. Zbl 0559.47039Solomyak, M. Z. 1 1983 On subspaces admitting a pseudodifferential projector. Zbl 0484.35085Birman, M. Sh.; Solomyak, M. Z. 11 1982 Asymptotics of the spectrum of variational problems on solutions of elliptic systems. Zbl 0501.35065Birman, M. Sh.; Solomyak, M. Z. 3 1982 Asymptotics of the spectrum of pseudodifferential operators with anisotropic-homogeneous symbols. Zbl 0492.47027Birman, M. Sh.; Solomyak, M. Z. 2 1982 Class of differential operators with abnormal behavior of the spectrum of the Dirichlet problem. Zbl 0515.35066Karol’, A. I.; Solomyak, M. Z. 1 1982 Asymptotics of the spectrum of variational problems on solutions of elliptic equations in unbounded domains. Zbl 0463.35061Birman, M. Sh.; Solomyak, M. Z. 7 1981 The asymptotics of the spectrum of the contact problem for second order elliptic equations. Zbl 0484.35065Karazeeva, N. A.; Solomyak, M. Z. 3 1981 Quantitative analysis in Sobolev imbedding theorems and applications to spectral theory. Transl. from the Russian by F. A. Cezus. Ed. by Lev J. Leifman. Zbl 0426.46020Birman, M. Sh.; Solomyak, M. Z. 50 1980 On spaces dual to the spaces \(\Lambda_\Omega\). Zbl 0438.46015Sajon, Ulare; Solomyak, M. Z. 1 1980 The asymptotics of the spectrum of pseudodifferential operators with anisotropic-homogeneous symbols. II. Zbl 0461.47025Birman, M. Sh.; Solomyak, M. Z. 1 1980 Asymptotic behavior of the spectrum of differential equations. Zbl 0424.35069Birman, M. Sh.; Solomyak, M. Z. 23 1979 ...and 51 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,011 Authors 56 Nazarov, Sergeĭ Aleksandrovich 44 Sukochev, Fedor Anatol’evich 37 Solomyak, Mikhaĭl Zakharovich 31 Peller, Vladimir Vsevolodovich 24 Birman, Mikhail Shlëmovich 18 Aleksandrov, Aleksei B. 17 Zanin, Dmitriy V. 15 Suslina, Tat’yana Aleksandrovna 15 Yafaev, Dimitri R. 14 Frank, Rupert L. 14 Sobolev, Alexander V. 13 Gesztesy, Fritz 13 Laptev, Ari 13 Pesenson, Isaac Zalmanovich 13 Potapov, Denis 13 Pushnitski, Alexander B. 11 Rozenblum, Grigori V. 11 Vasil’eva, Anastasiya Andreevna 10 Edmunds, David Eric 10 Malamud, Mark M. 10 Neidhardt, Hagen 10 Sheipak, Igor A. 10 Taskinen, Jari 9 Exner, Pavel 8 Ashyralyev, Allaberen 8 Carey, Alan L. 8 Ciarlet, Patrick jun. 8 Duan, Huoyuan 8 Ngai, Sze-Man 8 Skripka, Anna 8 Toft, Joachim 8 Verri, Alessandra A. 7 Agranovich, Mikhail Semënovich 7 Cardone, Giuseppe 7 de Oliveira, César R. 7 Galaktionov, Victor Aleksandrovich 7 Korotyaev, Evgeny L. 7 Kovařík, Hynek 7 Levendorskiĭ, Sergeĭ Zakharovich 7 McDonald, Edward Andrew 7 Melnikov, Yuri B. 7 Zou, Jun 6 Azamov, Nurulla A. 6 Bakharev, Fedor L’vovich 6 Behrndt, Jussi 6 Belishev, Mikhail Igorevitch 6 Borisov, Denis Ivanovich 6 Coine, Clement 6 Dauge, Monique 6 Dostanić, Milutin R. 6 Farforovskaya, Yuliya B. 6 Kostenko, Aleksey S. 6 Lang, Jan 6 Nazarov, Alexander I. 6 Ruotsalainen, Keijo Matti 6 Sloushch, Vladimir Anatolevich 6 Tan, Roger C. E. 6 Zakora, Dmitriĭ Aleksandrovich 5 Akturk, Sema 5 Costabel, Martin 5 Ekholm, Tomas 5 El Aidi, Mohammed 5 Grubb, Gerd 5 Hislop, Peter D. 5 Jocić, Danko R. 5 Kostrykin, Vadim V. 5 Krejčiřík, David 5 Le Merdy, Christian 5 Makarov, Konstantin A. 5 Nazaikinskii, Vladimir E. 5 Nazarov, Fedor L. 5 Nicaise, Serge 5 Pankrashkin, Konstantin 5 Rastegaev, N. V. 5 Shul’man, Viktor Semënovich 5 Simonov, Sergey A. 5 Tamura, Hideo 5 Tang, Wei 5 Tomskova, Anna 5 Triebel, Hans 5 Weidl, Timo 4 Boĭmatov, Kamoliddin Khamroevich 4 Buffa, Annalisa 4 Chattopadhyay, Arup 4 Chen, Junqing 4 Dobrokhotov, Sergei Yurievich 4 Faierman, Melvin 4 Fëdorov, Vladimir Evgen’evich 4 Filonov, Nikolai D. 4 Gómez, Delfina 4 Hiptmair, Ralf 4 Karuhanga, Martin 4 Kurasov, Pavel B. 4 Levin, Daniel 4 Levitina, Galina Borisovna 4 Maz’ya, Vladimir Gilelevich 4 Mugnolo, Delio 4 Pérez-martínez, María-eugenia 4 Plamenevskiĭ, Boris Alekseevich 4 Raikov, Georgi D. ...and 911 more Authors all top 5 Cited in 238 Serials 70 Journal of Functional Analysis 57 Journal of Mathematical Sciences (New York) 46 St. Petersburg Mathematical Journal 40 Journal of Soviet Mathematics 36 Functional Analysis and its Applications 32 Journal of Mathematical Physics 32 Mathematical Notes 32 Integral Equations and Operator Theory 31 Communications in Mathematical Physics 29 Journal of Mathematical Analysis and Applications 22 Advances in Mathematics 21 Siberian Mathematical Journal 17 Journal of Differential Equations 16 Proceedings of the American Mathematical Society 15 Transactions of the American Mathematical Society 15 Russian Journal of Mathematical Physics 15 Journal of Spectral Theory 13 Annales Henri Poincaré 12 Linear Algebra and its Applications 11 Ukrainian Mathematical Journal 11 Comptes Rendus. 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