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Solomyak, Mikhaĭl Zakharovich

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Author ID: solomyak.mikhail-zakharovich Recent zbMATH articles by "Solomyak, Mikhaĭl Zakharovich"
Published as: Solomyak, M. Z.; Solomyak, Michael; Solomyak, M.; Solomyak, Mikhaĭl Zakharovich
External Links: MGP · Math-Net.Ru
Documents Indexed: 174 Publications since 1953, including 4 Books
Biographic References: 3 Publications
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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

Publications by Year

Citations contained in zbMATH Open

151 Publications have been cited 1,710 times in 1,031 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 0744.47017
Birman, M. S.; Solomyak, M. Z.
136
1987
\(L_ 2\)-theory of the Maxwell operator in arbitrary domains. Zbl 0653.35075
Birman, M. Sh.; Solomyak, M. Z.
91
1987
Piecewise-polynomial approximations of functions of the class \(W_p^\alpha\). Zbl 0173.16001
Birman, M. Sh.; Solomyak, M. Z.
85
1967
Double operator integrals in a Hilbert space. Zbl 1054.47030
Birman, Mikhail Sh.; Solomyak, Michael
57
2003
Double Stieltjes operator integrals. II. Zbl 0182.46202
Birman, M. Sh.; Solomyak, M. Z.
56
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 0426.46020
Birman, M. Sh.; Solomyak, M. Z.
48
1980
On the spectrum of the Dirichlet Laplacian in a narrow strip. Zbl 1173.35090
Friedlander, Leonid; Solomyak, Michael
43
2009
Double Stieltjes operator integrals. Zbl 0161.34602
Birman, M. Sh.; Solomyak, M. Z.
43
1966
Estimates for the singular values of integral operators. Zbl 0344.47021
Birman, M. Sh.; Solomyak, M. Z.
39
1977
Estimates for the number of negative eigenvalues of the Schrödinger operator and its generalization. Zbl 0749.35026
Birman, M. Sh.; Solomyak, M. Z.
30
1991
Eigenvalue estimates for the weighted Laplacian on metric trees. Zbl 1046.34092
Naimark, K.; Solomyak, M.
30
2000
On a spectral problem related to self-similar measures. Zbl 0823.34071
Solomyak, M.; Verbitsky, E.
29
1995
Double Stieltjes operator integrals. III: Limit under the integral sign. Zbl 0281.47013
Birman, M. Sh.; Solomyak, M. Z.
27
1973
Estimates of singular numbers of integral operators. Zbl 0376.47023
Birman, M. Sh.; Solomyak, M. Z.
26
1977
Asymptotic behavior of the spectrum of pseudodifferential operators with anisotropically homogeneous symbols. Zbl 0377.47033
Birman, M. Sh.; Solomyak, M. Z.
25
1977
Spectral asymptotics of nonsmooth elliptic operators. I. Zbl 0251.35075
Birman, M. Sh.; Solomyak, M. Z.
25
1972
Estimates of the spectrum of a difference of fractional powers of selfadjoint operators. Zbl 0313.47020
Birman, M. Sh.; Koplienko, L. S.; Solomyak, M. Z.
25
1975
On the spectrum of narrow periodic waveguides. Zbl 1180.35392
Friedlander, L.; Solomyak, M.
24
2008
Remarks on the spectral shift function. Zbl 0329.47009
Birman, M. Sh.; Solomyak, M. Z.
24
1972
Remarks on the spectral shift function. Zbl 0336.47017
Birman, M. Sh.; Solomyak, M. Z.
23
1975
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 0803.47045
Solomyak, M.
23
1994
Schrödinger operators on homogeneous metric trees: spectrum in gaps. Zbl 1038.81023
Sobolev, Alexander V.; Solomyak, Michael
23
2002
On the spectrum of the Laplacian on regular metric trees. Zbl 1077.47513
Solomyak, Michael
23
2004
Boundedness conditions and spectrum estimates for the operators \(b (X) a (D)\) and their analogs. Zbl 0768.47025
Birman, M. Sh.; Karadzhov, G. E.; Solomyak, M. Z.
22
1991
The Rozenblum-Lieb-Cwikel inequality for Markov generators. Zbl 0910.47017
Levin, Daniel; Solomyak, Michael
21
1997
Schrödinger operator. Estimates for number of bound states as function- theoretical problem. Zbl 0756.35057
Birman, M. S.; Solomyak, M. Z.
20
1992
On the spectrum of the Dirichlet Laplacian in a narrow infinite strip. Zbl 1170.35487
Friedlander, Leonid; Solomyak, Michael
20
2008
Asymptotic behavior of the spectrum of differential equations. Zbl 0424.35069
Birman, M. Sh.; Solomyak, M. Z.
20
1979
The application of the semigroup theory to the study of differential equations in Banach spaces. Zbl 0090.09902
Solomyak, M. Z.
18
1958
Operator integration, perturbations and commutators. Zbl 0709.47022
Birman, M. Sh.; Solomyak, M. Z.
17
1989
Two-sided estimates on singular values for a class of integral operators on the semi-axis. Zbl 0817.47024
Newman, Joshua; Solomyak, Michael
16
1994
Tensor product of a finite number of spectral measures is always a spectral measure. Zbl 0844.47013
Birman, M.; Solomyak, M.
16
1996
Spectral theory of differential operators. Zbl 0715.35057
Rozenblyum, G. V.; Solomyak, M. Z.; Shubin, M. A.
15
1989
On approximation of functions from Sobolev spaces on metric graphs. Zbl 1027.46037
Solomyak, Michael
15
2003
Spectral theory of differential operators. Zbl 0805.35081
Rozenblyum, G. V.; Shubin, M. A.; Solomyak, M. Z.
14
1989
Asymptotics of the spectrum of variational problems on solutions of elliptic equations. Zbl 0427.35050
Birman, M. Sh.; Solomyak, M. Z.
14
1979
Asymptotic behavior of the spectrum of weakly polar integral operators. Zbl 0261.47027
Birman, M. Sh.; Solomyak, M. Z.
14
1971
Maxwell operator in regions with nonsmooth boundaries. Zbl 0655.35067
Birman, M. Sh.; Solomyak, M. Z.
13
1987
On the spectral estimates for the Schrödinger operator on \(\mathbb Z^d\), \(d \geqslant 3\). Zbl 1207.35237
Rozenblum, Grigori; Solomyak, Michael
13
2009
Geometry of Sobolev spaces on regular trees and the Hardy inequalities. Zbl 1187.46028
Naimark, K.; Solomyak, M.
12
2001
The eigenvalue behaviour for the boundary value problems related to self- similar measures on \(\mathbb{R}^ d\). Zbl 0836.60016
Naimark, K.; Solomyak, M.
12
1995
A remark on the Hardy inequalities. Zbl 0812.26007
Solomyak, Michael
12
1994
The self-adjoint Maxwell operator in arbitrary domains. Zbl 0733.35099
Birman, M. Sh.; Solomyak, M. Z.
12
1990
Counting Schrödinger boundstates: Semiclassics and beyond. Zbl 1172.35046
Rozenblum, Grigori; Solomyak, Michael
11
2009
The Weyl asymptotics of the spectrum of the Maxwell operator for domains with a Lipschitz boundary. Zbl 0639.35062
Birman, M. Sh.; Solomyak, M. Z.
11
1987
Regular and pathological eigenvalue behavior for the equation \(-\lambda u''=Vu\) on the semiaxis. Zbl 0895.34063
Naimark, K.; Solomyak, M.
10
1997
On subspaces admitting a pseudodifferential projector. Zbl 0484.35085
Birman, M. Sh.; Solomyak, M. Z.
10
1982
On the negative spectrum of the two-dimensional Schrödinger operator with radial potential. Zbl 1253.35037
Laptev, A.; Solomyak, M.
10
2012
The asymptotics of the spectrum of pseudo-differential operators with anisotropic-homogeneous symbols. II. Zbl 0439.47040
Birman, M. Sh.; Solomyak, M. Z.
10
1979
Leading term in the asymptotic spectral formula for ”nonsmooth” elliptic problems. Zbl 0225.35077
Birman, M. Sh.; Solomyak, M. Z.
10
1970
On eigenvalue estimates for the weighted Laplacian on metric graphs. Zbl 1045.35048
Solomyak, Michael
9
2002
On the eigenvalue behaviour for a class of differential operators on the semiaxis. Zbl 0916.34067
Birman, M. Sh.; Laptev, A.; Solomyak, M.
9
1998
On the negative discrete spectrum of a periodic elliptic operator in a waveguide-type domain, perturbed by a decaying potential. Zbl 1200.35196
Birman, M. Sh.; Solomyak, M.
9
2001
Product of commuting spectral measures need not be countably additive. Zbl 0423.28008
Birman, 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 0426.46019
Birman, M. Sh.; Solomyak, M. Z.
9
1974
Smilansky’s model of irreversible quantum graphs. I: The absolutely continuous spectrum. Zbl 1064.81037
Evans, W. D.; Solomyak, M.
9
2005
On principal eigenvalues for indefinite problems in Euclidean space. Zbl 0908.35085
Rozenblum, Grigori; Solomyak, Michael
8
1998
Spectral asymptotics of degenerate elliptic operators. Zbl 0268.35070
Vulis, I. L.; Solomyak, M. Z.
8
1972
The analytic nature of the semigroup generated by an elliptic operator in \(L_p\) spaces. Zbl 0087.11703
Solomyak, M. Z.
8
1959
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 0102.31501
Solomyak, M. Z.
8
1960
On spectral estimates for two-dimensional Schrödinger operators. Zbl 1294.35048
Laptev, Ari; Solomyak, Michael
8
2013
On spectral estimates for Schrödinger-type operators: the case of small local dimension. Zbl 1272.47055
Rozenblum, G. V.; Solomyak, M. Z.
8
2010
Asymptotics of the spectrum of the Schrödinger operator with nonregular homogeneous potential. Zbl 0657.35099
Solomyak, M. Z.
7
1986
Asymptotics of the spectrum of variational problems on solutions of elliptic equations in unbounded domains. Zbl 0463.35061
Birman, M. Sh.; Solomyak, M. Z.
7
1981
On the main singularities of the electric component of the electro- magnetic field in regions with screens. Zbl 0804.35127
Birman, M. Sh.; Solomyak, M. Z.
7
1993
Estimates of singular values of integral operators. III: Operators in unbounded domains. Zbl 0181.13601
Birman, M. Sh.; Solomyak, M. Z.
7
1969
On the asymptotic spectrum of ”nonsmooth” elliptic equations. Zbl 0226.35072
Birman, M. Sh.; Solomyak, M. Z.
7
1971
Spectral asymptotics of nonsmooth elliptic operators. II. Zbl 0281.35079
Birman, M. Sh.; Solomyak, M. Z.
7
1973
On the absolutely continuous spectrum in a model of an irreversible quantum graph. Zbl 1098.81036
Naboko, Sergey N.; Solomyak, Michael
7
2006
Construction in a piecewise smooth domain of a function of the class \(H^ 2\) from the value of the conormal derivative. Zbl 0696.46039
Birman, M. Sh.; Solomyak, M. Z.
6
1990
Spectral problems related to the critical exponent in the Sobolev embedding theorem. Zbl 0831.35116
Solomyak, M.
6
1995
On the eigenvalue behaviour for a class of operators related to self- similar measures on \(\mathbb{R}^ d\). Zbl 0808.60038
Naimark, Katherine; Solomyak, Michael
6
1994
Smilansky’s model of irreversible quantum graphs. II: The point spectrum. Zbl 1083.81519
Evans, W. D.; Solomyak, M.
6
2005
Spectral estimates for Schrödinger operators with sparse potentials on graphs. Zbl 1290.35284
Rozenblum, G.; Solomyak, M.
6
2011
Estimates of difference of fractional powers of selfadjoint operators in case of unbounded perturbations. Zbl 0709.47004
Birman, M. Sh.; Solomyak, M. Z.
5
1989
Asymptotics of the spectrum of pseudodifferential variational problems with restrictions. Zbl 0602.35086
Birman, M. S.; Solomyak, M. Z.
5
1986
Linear elliptic systems of the firs order. Zbl 0163.34602
Solomyak, M. Z.
5
1963
CLR-estimate revisited: Lieb’s approach with no path integrals. Zbl 1027.47020
Rozenblum, G.; Solomyak, M.
5
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 0876.35079
Birman, Mikhail Sh.; Laptev, Ari; Solomyak, Michael
5
1997
On a family of differential operators with the coupling parameter in the boundary condition. Zbl 1146.35064
Rozenblum, G.; Solomyak, M.
5
2007
The quantum graph as a limit of a network of physical wires. Zbl 1119.34026
Smilansky, Uzy; Solomyak, Michael
5
2006
Equivalent renormings of \(W_p^r\) classes in the case of partitioning of the domain. Zbl 0269.46024
Birman, M. Sh.; Solomyak, M. Z.
5
1973
Laplace and Schrödinger operators on regular metric trees: The discrete spectrum case. Zbl 1079.34065
Solomyak, Michael
5
2003
On the discrete spectrum of a family of differential operators. Zbl 1084.47038
Solomyak, M. Z.
5
2004
On the limiting behaviour of the spectra of a family of differential operators. Zbl 1105.35064
Solomyak, Michael
5
2006
On a mathematical model of irreversible quantum graphs. Zbl 1264.47051
Solomyak, M. Z.
5
2006
Asymptotics of the spectrum of the Schrödinger operator with a nonregular homogeneous potential. Zbl 0583.35083
Solomyak, M. Z.
4
1985
Compact operators with the power asymptotics of singular numbers. Zbl 0518.47014
Birman, M. Sh.; Solomyak, M. Z.
4
1983
CLR-estimate for the generators of positivity preserving and positively dominated semi-groups. Zbl 0911.47025
Rozenblyum, G.; Solomyak, M.
4
1997
Estimates of singular values of integral operators. II. Zbl 0177.18802
Birman, M. Sh.; Solomyak, M. Z.
4
1967
An estimate for Schur multipliers in \(S_ p\)-classes. Zbl 0806.15020
Olevskii, V.; Solomyak, M.
4
1994
Remarks on the nuclearity of integral operators and the boundedness of pseudodifferential operators. Zbl 0187.08501
Birman, M. Sh.; Solomyak, M. Z.
4
1969
Spectral asymptotics of nonsmooth elliptic operators. Zbl 0264.35056
Birman, M. Sh.; Solomyak, M. Z.
4
1972
Asymptotics of the spectrum of variational problems on solutions of elliptic systems. Zbl 0501.35065
Birman, M. Sh.; Solomyak, M. Z.
3
1982
On the number of negative eigenvalues for the two-dimensional magnetic Schrödinger operator. Zbl 0920.35101
Rozenblum, G.; Solomyak, M.
3
1999
Stieltjes double operator integrals and multiplier problems. Zbl 0177.18801
Birman, M. Sh.; Solomyak, M. Z.
3
1966
Negative discrete spectrum of the Schrödinger operator with large coupling constant: A qualitative discussion. Zbl 0746.35024
Birman, M. S.; Solomyak, M. Z.
3
1990
Über geometrische Charakteristiken der Einbettung von \(W^ \alpha_ p\)-Klassen in \(C\). Zbl 0156.36801
Solomyak, M. Z.; Tikhomirov, V. M.
3
1967
Estimates of singular values of integral operators. I. Zbl 0161.34701
Birman, M. Sh.; Solomyak, M. Z.
3
1967
Spectral asymptotics of nonsmooth elliptic operators. II. Zbl 0296.35066
Birman, M. Sh.; Solomyak, M. Z.
3
1975
On spectral estimates for two-dimensional Schrödinger operators. Zbl 1294.35048
Laptev, Ari; Solomyak, Michael
8
2013
On a class of spectral problems on the half-line and their applications to multi-dimensional problems. Zbl 1270.34197
Solomyak, Michael
3
2013
On the negative spectrum of the two-dimensional Schrödinger operator with radial potential. Zbl 1253.35037
Laptev, A.; Solomyak, M.
10
2012
On the mathematical work of M. Sh. Birman. Zbl 1236.01029
Solomyak, M. Z.; Suslina, T. A.; Yafaev, D. R.
1
2012
Spectral estimates for Schrödinger operators with sparse potentials on graphs. Zbl 1290.35284
Rozenblum, G.; Solomyak, M.
6
2011
On spectral estimates for Schrödinger-type operators: the case of small local dimension. Zbl 1272.47055
Rozenblum, G. V.; Solomyak, M. Z.
8
2010
Mikhail Shlemovich Birman (obituary). Zbl 1219.01025
Babich, 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 1173.35090
Friedlander, Leonid; Solomyak, Michael
43
2009
On the spectral estimates for the Schrödinger operator on \(\mathbb Z^d\), \(d \geqslant 3\). Zbl 1207.35237
Rozenblum, Grigori; Solomyak, Michael
13
2009
Counting Schrödinger boundstates: Semiclassics and beyond. Zbl 1172.35046
Rozenblum, Grigori; Solomyak, Michael
11
2009
Remarks on counting negative eigenvalues of the Schrödinger operator on regular metric trees. Zbl 1196.34037
Solomyak, Michael
2
2009
On the spectrum of narrow periodic waveguides. Zbl 1180.35392
Friedlander, L.; Solomyak, M.
24
2008
On the spectrum of the Dirichlet Laplacian in a narrow infinite strip. Zbl 1170.35487
Friedlander, Leonid; Solomyak, Michael
20
2008
On the scientific work of M. Sh. Birman in 1998–2007. Continuation of the list of publications of M. Sh. Birman. Zbl 1159.01011
Solomyak, M.; Suslina, T.
2
2008
On a family of differential operators with the coupling parameter in the boundary condition. Zbl 1146.35064
Rozenblum, G.; Solomyak, M.
5
2007
On the absolutely continuous spectrum in a model of an irreversible quantum graph. Zbl 1098.81036
Naboko, Sergey N.; Solomyak, Michael
7
2006
The quantum graph as a limit of a network of physical wires. Zbl 1119.34026
Smilansky, Uzy; Solomyak, Michael
5
2006
On the limiting behaviour of the spectra of a family of differential operators. Zbl 1105.35064
Solomyak, Michael
5
2006
On a mathematical model of irreversible quantum graphs. Zbl 1264.47051
Solomyak, M. Z.
5
2006
Smilansky’s model of irreversible quantum graphs. I: The absolutely continuous spectrum. Zbl 1064.81037
Evans, W. D.; Solomyak, M.
9
2005
Smilansky’s model of irreversible quantum graphs. II: The point spectrum. Zbl 1083.81519
Evans, W. D.; Solomyak, M.
6
2005
On the spectrum of the Laplacian on regular metric trees. Zbl 1077.47513
Solomyak, Michael
23
2004
On the discrete spectrum of a family of differential operators. Zbl 1084.47038
Solomyak, M. Z.
5
2004
On a differential operator appearing in the theory of irreversible quantum graphs. Zbl 1063.35124
Solomyak, Michael
2
2004
Mikhail Shlemovich Birman (on the occasion of his 75th birthday). Zbl 1061.01500
Buslaev, V. S.; Solomyak, M. Z.; Yafaev, D. R.
1
2004
Double operator integrals in a Hilbert space. Zbl 1054.47030
Birman, Mikhail Sh.; Solomyak, Michael
57
2003
On approximation of functions from Sobolev spaces on metric graphs. Zbl 1027.46037
Solomyak, Michael
15
2003
Laplace and Schrödinger operators on regular metric trees: The discrete spectrum case. Zbl 1079.34065
Solomyak, Michael
5
2003
Schrödinger operators on homogeneous metric trees: spectrum in gaps. Zbl 1038.81023
Sobolev, Alexander V.; Solomyak, Michael
23
2002
On eigenvalue estimates for the weighted Laplacian on metric graphs. Zbl 1045.35048
Solomyak, Michael
9
2002
Geometry of Sobolev spaces on regular trees and the Hardy inequalities. Zbl 1187.46028
Naimark, K.; Solomyak, M.
12
2001
On the negative discrete spectrum of a periodic elliptic operator in a waveguide-type domain, perturbed by a decaying potential. Zbl 1200.35196
Birman, M. Sh.; Solomyak, M.
9
2001
Eigenvalue distribution of some fractal semi-elliptic differential operators: Combinatorial approach. Zbl 0983.35096
Naimark, K.; Solomyak, M.
2
2001
A few words about V. A. Zalgaller. Zbl 1077.01533
Solomyak, M. Z.
1
2001
Eigenvalue estimates for the weighted Laplacian on metric trees. Zbl 1046.34092
Naimark, K.; Solomyak, M.
30
2000
Estimates for the approximation numbers of the weighted Riemann-Liouville operator in the spaces \(L_p\). Zbl 0976.47028
Solomyak, Michael
2
2000
Mikhail Shlyomovich Birman (on his 70th birthday). Zbl 0958.01026
Buslaev, 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 0920.35101
Rozenblum, G.; Solomyak, M.
3
1999
On the scientific work of Mikhail Shlëmovich Birman. List of publications of M. Sh. Birman. Zbl 1026.01503
Buslaev, V.; Solomyak, M.; Yafaev, D.
2
1999
Differential operators and spectral theory. M. Sh. Birman’s 70th anniversary collection. Zbl 0911.00011
Buslaev, V.; Solomyak, M.; Yafaev, D.
1
1999
On the eigenvalue behaviour for a class of differential operators on the semiaxis. Zbl 0916.34067
Birman, M. Sh.; Laptev, A.; Solomyak, M.
9
1998
On principal eigenvalues for indefinite problems in Euclidean space. Zbl 0908.35085
Rozenblum, Grigori; Solomyak, Michael
8
1998
On the discrete spectrum of a class of problems involving the Neumann Laplacian in unbounded domains. Zbl 0906.35065
Solomyak, Michael
2
1998
The Rozenblum-Lieb-Cwikel inequality for Markov generators. Zbl 0910.47017
Levin, Daniel; Solomyak, Michael
21
1997
Regular and pathological eigenvalue behavior for the equation \(-\lambda u''=Vu\) on the semiaxis. Zbl 0895.34063
Naimark, K.; Solomyak, M.
10
1997
CLR-estimate revisited: Lieb’s approach with no path integrals. Zbl 1027.47020
Rozenblum, G.; Solomyak, M.
5
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 0876.35079
Birman, Mikhail Sh.; Laptev, Ari; Solomyak, Michael
5
1997
CLR-estimate for the generators of positivity preserving and positively dominated semi-groups. Zbl 0911.47025
Rozenblyum, 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 0888.35075
Solomyak, Michael
1
1997
Tensor product of a finite number of spectral measures is always a spectral measure. Zbl 0844.47013
Birman, M.; Solomyak, M.
16
1996
On a spectral problem related to self-similar measures. Zbl 0823.34071
Solomyak, M.; Verbitsky, E.
29
1995
The eigenvalue behaviour for the boundary value problems related to self- similar measures on \(\mathbb{R}^ d\). Zbl 0836.60016
Naimark, K.; Solomyak, M.
12
1995
Spectral problems related to the critical exponent in the Sobolev embedding theorem. Zbl 0831.35116
Solomyak, M.
6
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 0803.47045
Solomyak, M.
23
1994
Two-sided estimates on singular values for a class of integral operators on the semi-axis. Zbl 0817.47024
Newman, Joshua; Solomyak, Michael
16
1994
A remark on the Hardy inequalities. Zbl 0812.26007
Solomyak, Michael
12
1994
On the eigenvalue behaviour for a class of operators related to self- similar measures on \(\mathbb{R}^ d\). Zbl 0808.60038
Naimark, Katherine; Solomyak, Michael
6
1994
An estimate for Schur multipliers in \(S_ p\)-classes. Zbl 0806.15020
Olevskii, V.; Solomyak, M.
4
1994
Eigenvalue estimates for a class of operators related to self-similar measures. Zbl 0881.58072
Solomyak, Michael
1
1994
My recollections of Ilya Bakelman. Zbl 0879.01031
Solomyak, Michael
1
1994
On the main singularities of the electric component of the electro- magnetic field in regions with screens. Zbl 0804.35127
Birman, M. Sh.; Solomyak, M. Z.
7
1993
Schrödinger operator. Estimates for number of bound states as function- theoretical problem. Zbl 0756.35057
Birman, M. S.; Solomyak, M. Z.
20
1992
On simultaneous action of Markov shift and adic transformation. Zbl 0771.28014
Solomyak, M.
2
1992
Estimates for the number of negative eigenvalues of the Schrödinger operator and its generalization. Zbl 0749.35026
Birman, M. Sh.; Solomyak, M. Z.
30
1991
Boundedness conditions and spectrum estimates for the operators \(b (X) a (D)\) and their analogs. Zbl 0768.47025
Birman, M. Sh.; Karadzhov, G. E.; Solomyak, M. Z.
22
1991
Viktor Abramovich Zalgaller (on his seventieth birthday). Zbl 0744.01010
Aleksandrov, 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 0748.35021
Birman, M. S.; Solomyak, M. Z.
1
1991
The self-adjoint Maxwell operator in arbitrary domains. Zbl 0733.35099
Birman, M. Sh.; Solomyak, M. Z.
12
1990
Construction in a piecewise smooth domain of a function of the class \(H^ 2\) from the value of the conormal derivative. Zbl 0696.46039
Birman, M. Sh.; Solomyak, M. Z.
6
1990
Negative discrete spectrum of the Schrödinger operator with large coupling constant: A qualitative discussion. Zbl 0746.35024
Birman, M. S.; Solomyak, M. Z.
3
1990
Operator integration, perturbations and commutators. Zbl 0709.47022
Birman, M. Sh.; Solomyak, M. Z.
17
1989
Spectral theory of differential operators. Zbl 0715.35057
Rozenblyum, G. V.; Solomyak, M. Z.; Shubin, M. A.
15
1989
Spectral theory of differential operators. Zbl 0805.35081
Rozenblyum, G. V.; Shubin, M. A.; Solomyak, M. Z.
14
1989
Estimates of difference of fractional powers of selfadjoint operators in case of unbounded perturbations. Zbl 0709.47004
Birman, M. Sh.; Solomyak, M. Z.
5
1989
Operator integration, perturbations, and commutators. Zbl 0784.47033
Birman, M. Sh.; Solomyak, M. Z.
2
1989
Estimates for the difference of fractional powers of selfadjoint operators in the case of unbounded perturbations. Zbl 0784.47011
Birman, 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 0744.47017
Birman, M. S.; Solomyak, M. Z.
136
1987
\(L_ 2\)-theory of the Maxwell operator in arbitrary domains. Zbl 0653.35075
Birman, M. Sh.; Solomyak, M. Z.
91
1987
Maxwell operator in regions with nonsmooth boundaries. Zbl 0655.35067
Birman, M. Sh.; Solomyak, M. Z.
13
1987
The Weyl asymptotics of the spectrum of the Maxwell operator for domains with a Lipschitz boundary. Zbl 0639.35062
Birman, M. Sh.; Solomyak, M. Z.
11
1987
Construction of a function of class \(H^ 2\) with given conormal derivative in a piecewise smooth domain. Zbl 0677.46042
Birman, M. Sh.; Solomyak, M. Z.
2
1987
Asymptotics of the spectrum of the Schrödinger operator with nonregular homogeneous potential. Zbl 0657.35099
Solomyak, M. Z.
7
1986
Asymptotics of the spectrum of pseudodifferential variational problems with restrictions. Zbl 0602.35086
Birman, M. S.; Solomyak, M. Z.
5
1986
Asymptotics of the spectrum of the Schrödinger operator with a nonregular homogeneous potential. Zbl 0583.35083
Solomyak, M. Z.
4
1985
Asymptotic behavior of the spectrum of variational problems on the solutions of elliptic systems. Zbl 0562.35064
Birman, M. Sh.; Solomyak, M. Z.
1
1985
Application of interpolation methods to estimates of the spectrum of integral operators. Zbl 0606.46047
Birman, 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 0588.35069
Solomyak, M. Z.
2
1984
Compact operators whose singular numbers have powerlike asymptotics. Zbl 0546.47010
Birman, M. Sh.; Solomyak, M. Z.
1
1984
Compact operators with the power asymptotics of singular numbers. Zbl 0518.47014
Birman, M. Sh.; Solomyak, M. Z.
4
1983
On the Calderon projector. Zbl 0559.47039
Solomyak, M. Z.
1
1983
On subspaces admitting a pseudodifferential projector. Zbl 0484.35085
Birman, M. Sh.; Solomyak, M. Z.
10
1982
Asymptotics of the spectrum of variational problems on solutions of elliptic systems. Zbl 0501.35065
Birman, M. Sh.; Solomyak, M. Z.
3
1982
Asymptotics of the spectrum of pseudodifferential operators with anisotropic-homogeneous symbols. Zbl 0492.47027
Birman, M. Sh.; Solomyak, M. Z.
2
1982
Class of differential operators with abnormal behavior of the spectrum of the Dirichlet problem. Zbl 0515.35066
Karol’, A. I.; Solomyak, M. Z.
1
1982
Asymptotics of the spectrum of variational problems on solutions of elliptic equations in unbounded domains. Zbl 0463.35061
Birman, M. Sh.; Solomyak, M. Z.
7
1981
The asymptotics of the spectrum of the contact problem for second order elliptic equations. Zbl 0484.35065
Karazeeva, N. A.; Solomyak, M. Z.
2
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 0426.46020
Birman, M. Sh.; Solomyak, M. Z.
48
1980
On spaces dual to the spaces \(\Lambda_\Omega\). Zbl 0438.46015
Sajon, Ulare; Solomyak, M. Z.
1
1980
The asymptotics of the spectrum of pseudodifferential operators with anisotropic-homogeneous symbols. II. Zbl 0461.47025
Birman, M. Sh.; Solomyak, M. Z.
1
1980
Asymptotic behavior of the spectrum of differential equations. Zbl 0424.35069
Birman, M. Sh.; Solomyak, M. Z.
20
1979
...and 51 more Documents
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Cited by 935 Authors

53 Nazarov, Sergeĭ Aleksandrovich
38 Sukochev, Fedor Anatol’evich
37 Solomyak, Mikhaĭl Zakharovich
31 Peller, Vladimir Vsevolodovich
24 Birman, Mikhail Shlëmovich
18 Aleksandrov, Aleksei B.
15 Zanin, Dmitriy V.
14 Pushnitski, Alexander B.
13 Frank, Rupert L.
13 Sobolev, Alexander V.
13 Suslina, Tat’yana Aleksandrovna
12 Pesenson, Isaac Zalmanovich
12 Potapov, Denis
11 Laptev, Ari
11 Vasil’eva, Anastasiya Andreevna
11 Yafaev, Dimitri R.
10 Edmunds, David Eric
10 Gesztesy, Fritz
10 Malamud, Mark M.
10 Neidhardt, Hagen
10 Taskinen, Jari
9 Sheipak, Igor A.
8 Ciarlet, Patrick jun.
8 Duan, Huoyuan
8 Exner, Pavel
8 Skripka, Anna
7 Agranovich, Mikhail Semënovich
7 Ashyralyev, Allaberen
7 Cardone, Giuseppe
7 Carey, Alan L.
7 de Oliveira, César R.
7 Galaktionov, Victor Aleksandrovich
7 Korotyaev, Evgeny L.
7 Kovařík, Hynek
7 Levendorskiĭ, Sergeĭ Zakharovich
7 Ngai, Sze-Man
7 Toft, Joachim
7 Verri, Alessandra A.
6 Azamov, Nurulla A.
6 Bakharev, Fedor L’vovich
6 Belishev, Mikhail Igorevitch
6 Borisov, Denis Ivanovich
6 Dauge, Monique
6 Dostanić, Milutin R.
6 Farforovskaya, Yuliya B.
6 Lang, Jan
6 Melnikov, Yuri B.
6 Ruotsalainen, Keijo Matti
6 Sloushch, Vladimir Anatolevich
6 Tan, Roger C. E.
6 Zou, Jun
5 Costabel, Martin
5 Ekholm, Tomas
5 El Aidi, Mohammed
5 Grubb, Gerd
5 Hislop, Peter D.
5 Kostrykin, Vadim V.
5 Krejčiřík, David
5 Makarov, Konstantin A.
5 Nazaikinskii, Vladimir E.
5 Nazarov, Fedor L.
5 Nicaise, Serge
5 Pankrashkin, Konstantin
5 Rastegaev, N. V.
5 Rozenblum, Grigori V.
5 Shul’man, Viktor Semënovich
5 Tamura, Hideo
5 Tomskova, Anna
5 Triebel, Hans
5 Weidl, Timo
4 Akturk, Sema
4 Behrndt, Jussi
4 Boĭmatov, Kamoliddin Khamroevich
4 Buffa, Annalisa
4 Chen, Junqing
4 Coine, Clement
4 Dobrokhotov, Sergei Yurievich
4 Karuhanga, Martin
4 Kostenko, Aleksey S.
4 Kurasov, Pavel B.
4 Le Merdy, Christian
4 Levin, Daniel
4 Maz’ya, Vladimir Gilelevich
4 Mcdonald, Edward A.
4 Mugnolo, Delio
4 Nazarov, Alexander I.
4 Raikov, Georgi D.
4 Simonov, Sergey A.
4 Todorov, Ivan G.
4 Turowska, Lyudmila B.
4 Vladimirov, Anton A.
4 Yurko, Vjacheslav Anatoljevich
3 Anikin, A. Yu.
3 Brenner, Susanne Cecelia
3 Breuer, Jonathan
3 Brown, B. Malcolm
3 Camus, Brice
3 Chattopadhyay, Arup
3 Demchenko, Maxim Nikolaevich
3 Faierman, Melvin
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Cited in 217 Serials

63 Journal of Functional Analysis
50 Journal of Mathematical Sciences (New York)
42 St. Petersburg Mathematical Journal
40 Journal of Soviet Mathematics
32 Mathematical Notes
31 Journal of Mathematical Physics
30 Communications in Mathematical Physics
30 Integral Equations and Operator Theory
29 Functional Analysis and its Applications
26 Journal of Mathematical Analysis and Applications
21 Siberian Mathematical Journal
19 Advances in Mathematics
16 Proceedings of the American Mathematical Society
14 Transactions of the American Mathematical Society
13 Journal of Differential Equations
13 Russian Journal of Mathematical Physics
12 Annales Henri Poincaré
11 Ukrainian Mathematical Journal
11 Linear Algebra and its Applications
11 Comptes Rendus. Mathématique. Académie des Sciences, Paris
11 Journal of Spectral Theory
10 The Annals of Statistics
10 Journal of Approximation Theory
9 Computational Mathematics and Mathematical Physics
9 Boundary Value Problems
8 Applicable Analysis
8 Mathematische Annalen
7 Journal d’Analyse Mathématique
7 Mathematics of Computation
7 Reviews in Mathematical Physics
7 Numerische Mathematik
7 Zeitschrift für Analysis und ihre Anwendungen
7 Journal of Complexity
7 Communications in Partial Differential Equations
7 Journal de Mathématiques Pures et Appliquées. Neuvième Série
6 Journal of Statistical Physics
6 Mathematical Methods in the Applied Sciences
6 Duke Mathematical Journal
6 Journal of Computational and Applied Mathematics
6 Mathematische Nachrichten
6 Annales de l’Institut Henri Poincaré. Physique Théorique
6 Revista Matemática Complutense
5 Archive for Rational Mechanics and Analysis
5 Computers & Mathematics with Applications
5 Arkiv för Matematik
5 SIAM Journal on Numerical Analysis
5 Tohoku Mathematical Journal. Second Series
5 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
5 Sbornik: Mathematics
5 The Journal of Fourier Analysis and Applications
5 Doklady Mathematics
5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
5 Abstract and Applied Analysis
5 Mathematical Physics, Analysis and Geometry
5 Communications in Contemporary Mathematics
5 Proceedings of the Steklov Institute of Mathematics
4 Israel Journal of Mathematics
4 Reports on Mathematical Physics
4 Annals of Global Analysis and Geometry
4 Applied and Computational Harmonic Analysis
4 Bulletin des Sciences Mathématiques
4 Izvestiya: Mathematics
4 Journal of Inequalities and Applications
4 Journal of the European Mathematical Society (JEMS)
4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
3 Rocky Mountain Journal of Mathematics
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3 The Journal of Geometric Analysis
3 Bulletin of the American Mathematical Society. New Series
3 Potential Analysis
3 Calculus of Variations and Partial Differential Equations
3 Integral Transforms and Special Functions
3 Bernoulli
3 Differential Equations
3 Journal of Evolution Equations
3 Foundations of Computational Mathematics
3 Analysis and Applications (Singapore)
3 Advances in Difference Equations
3 Bulletin of Mathematical Sciences
2 Computer Methods in Applied Mechanics and Engineering
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2 Journal of Computational Physics
2 Letters in Mathematical Physics
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2 Applied Mathematics and Computation
2 Mathematische Zeitschrift
2 Mathematika
2 Systems & Control Letters
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Cited in 51 Fields

478 Partial differential equations (35-XX)
425 Operator theory (47-XX)
133 Quantum theory (81-XX)
127 Functional analysis (46-XX)
102 Ordinary differential equations (34-XX)
76 Optics, electromagnetic theory (78-XX)
72 Numerical analysis (65-XX)
62 Global analysis, analysis on manifolds (58-XX)
60 Approximations and expansions (41-XX)
41 Statistical mechanics, structure of matter (82-XX)
39 Harmonic analysis on Euclidean spaces (42-XX)
34 Mechanics of deformable solids (74-XX)
31 Integral equations (45-XX)
31 Fluid mechanics (76-XX)
30 Probability theory and stochastic processes (60-XX)
27 Statistics (62-XX)
25 Combinatorics (05-XX)
25 Real functions (26-XX)
21 Calculus of variations and optimal control; optimization (49-XX)
19 Potential theory (31-XX)
14 Measure and integration (28-XX)
12 Information and communication theory, circuits (94-XX)
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2 Algebraic geometry (14-XX)
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