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36 results on '"M. Z. Solomyak"'

1. On the mathematical work of M. Sh. Birman

Author

M. Z. Solomyak, Dmitrii Rauel'evich Yafaev, and Tatiana Aleksandrovna Suslina

Subjects
Work (thermodynamics), Algebra and Number Theory, Spectral theory, Transform theory, Function space, Applied Mathematics, 010102 general mathematics, Mathematical analysis, 01 natural sciences, Algebra, 0103 physical sciences, 010307 mathematical physics, Scattering theory, 0101 mathematics, Analysis, Mathematics
Published
2012

2. Eleven Papers in Analysis

Author

P. L. Shabalin, V. A. Zmorovich, A. A. Yakubenko, V. A. Pokhilevich, M. G. Kreĭn, A. A. Nudel′man, S. G. Kreĭn, G. A. Kurina, G. G. Gevorkyan, A. I. Saginashvili, M. Sh. Birman, M. Z. Solomyak, L. V. Mikaelyan, V. V. Ivanov, G. N. Kotenkova, M. Ya. Ivanov, V. V. Koretskii, N. Ya. Kurochkina, P. L. Shabalin, V. A. Zmorovich, A. A. Yakubenko, V. A. Pokhilevich, M. G. Kreĭn, A. A. Nudel′man, S. G. Kreĭn, G. A. Kurina, G. G. Gevorkyan, A. I. Saginashvili, M. Sh. Birman, M. Z. Solomyak, L. V. Mikaelyan, V. V. Ivanov, G. N. Kotenkova, M. Ya. Ivanov, V. V. Koretskii, and N. Ya. Kurochkina

Abstract

This collection of eleven papers covers a broad spectrum of topics in analysis, from the study of certain classes of analytic functions to the solvability of singular problems for differential and integral equations to computational schemes for the partial differential equations and singular integral equations.

Published
2016

3. Mikhail Shlemovich Birman (obituary)

Author

Lyudvig D Faddeev, Semen Grigor'evich Gindikin, Boris Plamenevskii, Anatolii Moiseevich Vershik, Nikolai K. Nikol’skii, M. Z. Solomyak, Victor Petrovich Havin, Nina Uraltseva, Leonid Pastur, Dmitrii Rauel'evich Yafaev, Serguei Vital'evich Kislyakov, Tatiana Aleksandrovna Suslina, Vladimir Alexandrovich Marchenko, Ari Laptev, Vladimir Buslaev, and Vasilii Mikhailovich Babich

Subjects
General Mathematics, Obituary, Theology, Mathematics
Published
2010

4. Михаил Шлемович Бирман (некролог)

Author

Serguei Vital'evich Kislyakov, Victor Petrovich Havin, Nikolai K. Nikol’skii, Leonid Pastur, Nina Nikolaevna Ural'tseva, Vasilii Mikhailovich Babich, Dmitrii Rauel'evich Yafaev, Anatolii Moiseevich Vershik, Semen Grigor'evich Gindikin, Boris Plamenevskii, M. Z. Solomyak, Tatiana Aleksandrovna Suslina, Lyudvig Dmitrievich Faddeev, Vladimir Savel'evich Buslaev, Vladimir Alexandrovich Marchenko, and Ari Laptev

Subjects
Philosophy, Theology, Obituary
Published
2010

6. On a mathematical model of irreversible quantum graphs

Author

M. Z. Solomyak

Subjects
Algebra and Number Theory, Applied Mathematics, Quantum graph, Quantum process, Spectrum (functional analysis), Mathematical analysis, Quantum operation, Quantum phase estimation algorithm, Quantum algorithm, Statistical physics, Quantum dissipation, Analysis, Mathematics
Published
2006

10. Obituary: Mikhail Birman, 17.01.1928-2.07.2009

Author

M. Z. Solomyak, T. Suslina, Dmitrii Rauel'evich Yafaev, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)

Subjects
Applied Mathematics, Philosophy, Obituary, 01 natural sciences, 010305 fluids & plasmas, 010101 applied mathematics, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], 01A70, 47-03, Modeling and Simulation, 0103 physical sciences, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Theology, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2010

11. Anatolii Moiseevich Vershik (on his sixtieth birthday)

Author

I M Gel'fand, Olga Aleksandrovna Ladyzhenskaya, Yakov G. Sinai, Vladimir I. Arnold, Il'dar Abdullovich Ibragimov, Andrei Aleksandrovich Lodkin, Lyudvig D Faddeev, A A Kirillov, S V Kerov, M Sh Birman, M. Z. Solomyak, S. P. Novikov, and Gennady A. Leonov

Subjects
General Mathematics, Theology, Mathematics
Published
1994

12. Operator integration, perturbations, and commutators

Author

M. Z. Solomyak and M. Sh. Birman

Subjects
Statistics and Probability, Combinatorics, symbols.namesake, Operator (computer programming), Applied Mathematics, General Mathematics, Mathematical analysis, Hilbert space, symbols, Mathematics::Representation Theory, Lambda, Spectral measure, Mathematics
Abstract

Under mild assumption, integral representations of the form (*) $$f(A_1 ) \cdot \mathfrak{J} - \mathfrak{J} \cdot f(A_1 ) = \int {\int {\frac{{f(\mu ) - f(\lambda )}}{{\mu - \lambda }}} } dE_1 (\mu )(A_1 \mathfrak{J} - \mathfrak{J}A_0 )dE_0 (\mu ),$$ are justified. Here Ak, k=0, 1, is a self-adjoint operator in a Hilbert space Hk, is an operator from H0 H1; in general, all the operators are unbounded; Ek is the spectral measure of the operator Ak. On the basis of the representation (*), estimates of the s-numbers of the operator $$f(A_1 ) \cdot \mathfrak{J} - \mathfrak{J} \cdot f(A_0 )$$ in terms of the s-numbers of the operator $$A_1 \mathfrak{J} - \mathfrak{J}A_0$$ are given. Analogous results are obtained for commutators and antocommutators.

Published
1993

13. Estimates for the difference of fractional powers of selfadjoint operators in the case of unbounded perturbations

Author

M. Z. Solomyak and M. Sh. Birman

Subjects
Statistics and Probability, Constant coefficients, Applied Mathematics, General Mathematics, Mathematical analysis, Microlocal analysis, Hilbert space, Spectral theorem, Operator theory, Compact operator on Hilbert space, Fourier integral operator, symbols.namesake, symbols, Operator norm, Mathematics
Abstract

Let A0, A1 be positive selfadjoint operators in a Hilbert space, let |·| be the norm in some symmetrically normed ideal of operators, satisjying the majorization condition. In the paper one obtains estimate and also some of its generalizations. Examples, with A0, A1 differential operators, are considered.

Published
1992

15. Construction in a piecewise smooth domain of a function of the class H2 from the value of the conormal derivative

Author

M. Sh. Birman and M. Z. Solomyak

Subjects
Statistics and Probability, Domain of a function, Applied Mathematics, General Mathematics, Bounded function, Mathematical analysis, Piecewise, Boundary (topology), Vector field, Function (mathematics), Lipschitz continuity, Domain (mathematical analysis), Mathematics
Abstract

The problem of the construction in a bounded domain Ω ⊂ ℝm with a Lipschitz boundary of a function Φ ∃ H2(Ω), for which the conormal derivative on ∂Ω coincides with the normal component of a given vector field u ∃ H1(Ω,C3), is discussed. The solution of this problem is given for piecewise smooth boundaries in the case m=3.

Published
1990

17. Ольга Александровна Ладыженская (некролог)

Author

Vsevolod Alekseevich Solonnikov, Yakov Grigor'evich Sinai, M. Birman, Victor Pavlovich Maslov, Lyudvig Dmitrievich Faddeev, Marko Iosifovich Vishik, Grigorii Aleksandrovich Seregin, Sergei Petrovich Novikov, Vladimir I. Arnold, Anatolii Moiseevich Vershik, Nina Nikolaevna Ural'tseva, Il'dar Abdullovich Ibragimov, Izrail Moiseevich Gel'fand, M. Z. Solomyak, and Григорий Александрович Серeгин

Subjects
Philosophy, Theology, Obituary
Published
2004

19. On the Discrete Spectrum of a Family of Differential Operators.

Author

M. Z. Solomyak

Abstract

We consider a family \mathbf{A}_/math> of differential operators in L^2(\mathbb{R}^2) depending on a parameter \alpha\ge 0. The operator \mathbf{A}_/math> formally corresponds to the quadratic form \mathbf{a}_\alpha[U]=\int_{\mathbb{R}^2}(|U_x|^2+\frac{1}{2}(|U_y|^2+y^2|U|^2))\,dx\,dy+\alpha\int_{\mathbb{R}}y|U(0,y)|^2\,dy. The perturbation determined by the second term in this sum is only relatively bounded but not relatively compact with respect to the unperturbed quadratic form $\mathbf{a}_0$.The spectral properties of $\mathbf{A}_\alpha$ strongly depend on $\alpha$. In particular, $\sigma(\mathbf{A}_0)=[1/2,\infty); for 0\textless\alpha\textless\sqrt 2, finitely many eigenvalues \lambda_n\textless1/2 are added to the spectrum; and for \alpha\textless\sqrt2 (where the quadratic form approach does not apply), the spectrum is purely continuous and coincides with \mathbb{R}. We study the asymptotic behavior of the number of eigenvalues as \alpha\nearrow\sqrt2 and reduce this problem to the problem on the spectral asymptotics for a certain Jacobi matrix. [ABSTRACT FROM AUTHOR]

Published
2004

24. Remarks on the spectral shift function

Author

M. Sh. Birman and M. Z. Solomyak

Subjects
Statistics and Probability, Applied Mathematics, General Mathematics, Quantum mechanics, Function (mathematics), Spectral shift, Mathematics
Published
1975

25. ASYMPTOTICS OF THE SPECTRUM OF THE SCHRÖDINGER OPERATOR WITH NONREGULAR HOMOGENEOUS POTENTIAL

Author

M Z Solomyak

Subjects
symbols.namesake, Homogeneous, General Mathematics, Operator (physics), Mathematical analysis, Spectrum (functional analysis), symbols, Computer Science::Formal Languages and Automata Theory, Schrödinger's cat, Mathematical physics, Mathematics
Abstract

Formulas are proved for the spectral asymptotics of a multidimensional Schrodinger operator with potential which behaves nonregularly at infinity.Bibliography: 17 titles.

Published
1986

26. ESTIMATES OF SINGULAR NUMBERS OF INTEGRAL OPERATORS

Author

M Sh Birman and M. Z. Solomyak

Subjects
Discrete mathematics, Pure mathematics, Kernel (algebra), Operator (computer programming), Homogeneous, Function space, General Mathematics, Bilinear interpolation, Interpolation, Mathematics
Abstract

ContentsIntroduction § 1. Operator spaces and function spaces § 2. Estimates of singular numbers based on the method of piecewise-polynomial approximation § 3. Interpolation methods § 4. General results on estimates (statements) § 5. Proof of the main results on estimates § 6. Operators with a difference kernel § 7. Tests for nuclearity § 8. Multipliers in classes of kernels of integral operators § 9. Analytical results for the multiplier problem § 10. Operators with a homogeneous difference kernel § 11. Some special casesAppendix. M. Z. Solomyak, The Interpolation of bilinear maps from function spaces into operator spacesReferences

Published
1977

27. L2-Theory of the Maxwell operator in arbitrary domains

Author

M. Z. Solomyak and M Sh Birman

Subjects
Pure mathematics, Operator (computer programming), General Mathematics, Bounded function, Mathematical analysis, Boundary (topology), Boundary value problem, Lipschitz continuity, Mathematics, Discrete spectrum
Abstract

CONTENTSIntroduction § 1. Classes of functions. Boundary conditions § 2. Definition of the Maxwell operator. Inclusion in the elliptic theory § 3. Bounded domains with Lipschitz boundary § 4. Domains with piecewise-smooth boundary § 5. Asymptotic properties of the discrete spectrum of the operator § 6. Comments and bibliographic notes References

Published
1987

28. Asymptotic behavior of the spectrum of variational problems on the solutions of elliptic systems

Author

M. Sh. Birman and M. Z. Solomyak

Subjects
Statistics and Probability, Elliptic curve point multiplication, Quarter period, Applied Mathematics, General Mathematics, Mathematical analysis, Boundary problem, Elliptic rational functions, Free boundary problem, Boundary (topology), Boundary value problem, Mathematics, Jacobi elliptic functions
Abstract

One computes the principal term of the asymptotics of the spectrum of variational problems of the form B[u]/A[u] considered on the solutions of elliptic systems Lu=0 on a compact manifold with boundary. Previously, the corresponding result has been obtained by the authors under the additional condition of the existence of an elliptic boundary problem for the operator L. Now this restriction is removed.

Published
1985

31. Mikhail Shlëmovich Birman (on his sixtieth birthday)

Author

M. Z. Solomyak, Olga Aleksandrovna Ladyzhenskaya, I M Gel'fand, Boris Pavlov, Dmitrii Rauel'evich Yafaev, Vladimir Savel'evich Buslaev, and Lyudvig D Faddeev

Subjects
General Mathematics, Theology, Mathematics
Published
1988

32. On One Class of Stieltjes Multiple-Integral Operators

Author

M. Z. Solomyak and V. V. Sten’kin

Subjects
Class (set theory), Pure mathematics, Operator (computer programming), Laplace–Stieltjes transform, Multiple integral, Riemann–Stieltjes integral, Operator theory, Variety (universal algebra), Mathematics, Connection (mathematics)
Abstract

The concept of a Stieltjes multiple-integral operator was first introduced by Yu. L. Daletskii and S. G. Krein [1] in connection with certain aspects of analytical perturbation theory. In a number of articles [2–5], M. Sh. Birman and M. Z. Solomyak developed the theory of double-integral operators which they found to be closely related to a variety of problems in analysis.

Published
1971

33. Double-Integral Operators in the Ring $$ \mathop R\limits^ \wedge $$

Author

M. Z. Solomyak

Subjects
Physics, Multiple integral, Essential spectrum, Lambda, Wedge (geometry), Spectral measure, Mathematical physics, Symmetric operator
Abstract

1. This article is devoted to a study of double-integral operators of the form $$ \int\limits_A {\int\limits_M {f(\lambda ,\mu )F(d\mu )TE(d\lambda )} } $$ (1)

Published
1969

34. Stieltjes Double-Integral Operators

Author

M. Z. Solomyak and M. Sh. Birman

Subjects
Physics, Pure mathematics, Volterra operator, Multiple integral, Riemann–Stieltjes integral, Type (model theory), Lambda, Separable hilbert space
Abstract

In the present paper we investigate operators in separable Hilbert space H given by integrals of the type $$ Q = \int {\int \varphi } \left( {\lambda ,\mu } \right)d{F_\mu }Td{E_\lambda }. $$ (1.1)

Published
1967

36. On the asymptotic spectrum of 'nonsmooth' elliptic equations

Author

M. Sh. Birman and M. Z. Solomyak

Subjects
Quarter period, Elliptic partial differential equation, Modular elliptic curve, Applied Mathematics, Mathematical analysis, Elliptic rational functions, Elliptic integral, Schoof's algorithm, Supersingular elliptic curve, Analysis, Mathematics, Jacobi elliptic functions
Published
1971

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