On the mathematical work of Mikhail Zakharovich Solomyak

DOI10.1090/spmj/1548zbMath1436.47001OpenAlexW2938268105WikidataQ128057248 ScholiaQ128057248MaRDI QIDQ5743349

Publication date: 9 May 2019

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/spmj/1548

zbMATH Keywords

perturbation theory spectral asymptotics Schur multipliers double operator integrals piecewise-polynomial approximation

Mathematics Subject Classification ID

Biographies, obituaries, personalia, bibliographies (01A70) Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of partial differential operators (47F05) History of operator theory (47-03) History of partial differential equations (35-03)

Cites Work

On spectral estimates for Schrödinger-type operators: the case of small local dimension
On spectral estimates for two-dimensional Schrödinger operators
On the negative spectrum of the two-dimensional Schrödinger operator with radial potential
On the spectral estimates for the Schrödinger operator on $\mathbb Z^d$, $d \geqslant 3$
Linear and complex analysis. Problem book. 199 research problems
On the spectrum of the Dirichlet Laplacian in a narrow strip
Geometry of Sobolev spaces on regular trees and the Hardy inequalities
On the spectrum of narrow periodic waveguides
Class of differential operators with abnormal behavior of the spectrum of the Dirichlet problem
Maxwell operator in regions with nonsmooth boundaries
Product of commuting spectral measures need not be countably additive
Asymptotic behavior of the spectrum of differential equations
Asymptotics of the spectrum of variational problems on solutions of elliptic equations
Asymptotics of the spectrum of variational problems on solutions of elliptic equations in unbounded domains
Piecewise-polynomial approximation of functions from $H^ \ell((0,1)^ d)$, $2\ell=d$, and applications to the spectral theory of the Schrödinger operator
A remark on the Hardy inequalities
An estimate for Schur multipliers in $S_ p$-classes
Two-sided estimates on singular values for a class of integral operators on the semi-axis
The negative discrete spectrum of the operator $(-\Delta)^ l-\alpha V$ in $L_ 2(\mathbb{R}^ d)$ for $d$ even and $2l\geq d$
The Rozenblum-Lieb-Cwikel inequality for Markov generators
Regular and pathological eigenvalue behavior for the equation $-\lambda u=Vu$ on the semiaxis
Double operator integrals in a Hilbert space
A few words about V. A. Zalgaller
On approximation of functions from Sobolev spaces on metric graphs
The eigenvalue behaviour for the boundary value problems related to self- similar measures on $\mathbb{R}^ d$
Tensor product of a finite number of spectral measures is always a spectral measure
On a class of spectral problems on the half-line and their applications to multi-dimensional problems
Spectral estimates for Schrödinger operators with sparse potentials on graphs
On a family of differential operators with the coupling parameter in the boundary condition
On the discrete spectrum of a family of differential operators
Leading term in the asymptotic spectral formula for nonsmooth elliptic problems
On the asymptotic spectrum of nonsmooth elliptic equations
On spectral estimates for the Schrödinger operators in global dimension 2
Mikhail Shlemovich Birman (obituary)
On the mathematical work of M. Sh. Birman
ON THE ABSOLUTELY CONTINUOUS SPECTRUM IN A MODEL OF AN IRREVERSIBLE QUANTUM GRAPH
Counting Schrödinger Boundstates: Semiclassics and Beyond
Application of interpolation methods to estimates of the spectrum of integral operators
L₂-Theory of the Maxwell operator in arbitrary domains
ASYMPTOTICS OF THE SPECTRUM OF THE SCHRÖDINGER OPERATOR WITH NONREGULAR HOMOGENEOUS POTENTIAL
On Principal Eigenvalues for Indefinite Problems in Euclidean Space
Viktor Abramovich Zalgaller (on his seventieth birthday)
Schrödinger operator. Estimates for number of bound states as function-theoretical problem
SPECTRAL ASYMPTOTICS OF SECOND-ORDER DEGENERATE ELLIPTIC OPERATORS
ESTIMATES OF SINGULAR NUMBERS OF INTEGRAL OPERATORS
On the Eigenvalue Behaviour for a Class of Differential Operators on Semiaxis
SCHRÖDINGER OPERATORS ON HOMOGENEOUS METRIC TREES: SPECTRUM IN GAPS
Eigenvalue Estimates for the Weighted Laplacian on Metric Trees
Mikhail Shlyomovich Birman (on his 70th birthday)
Mikhail Shlemovich Birman \lowercase{(on the occasion of his 75th birthday)}
Olga Aleksandrovna Ladyzhenskaya (obituary)
Smilansky's model of irreversible quantum graphs: I. The absolutely continuous spectrum
Spectral Problems Related to the Critical Exponent in the Sobolev Embedding Theorem
On a Spectral Problem Related to Self-Similar Measures
Chebyshev-Haar systems in the theory of discontinuous Kellogg kernels
Remarks on counting negative eigenvalues of Schr\"odinger operator on regular metric trees
Vitali Liskevich
On the spectrum of the Laplacian on regular metric trees
On a differential operator appearing in the theory of irreversible quantum graphs
On the limiting behaviour of the spectra of a family of differential operators
On a mathematical model of irreversible quantum graphs
PIECEWISE-POLYNOMIAL APPROXIMATIONS OF FUNCTIONS OF THE CLASSES $ W_{p}^{\alpha}$
ON EXISTENCE CONDITIONS FOR THE STIELTJES INTEGRAL
ASYMPTOTIC BEHAVIOR OF THE SPECTRUM OF WEAKLY POLAR INTEGRAL OPERATORS
Smilansky's model of irreversible quantum graphs: II. The point spectrum
On the negative discrete spectrum of a periodic elliptic operator in a waveguide-type domain, perturbed by a decaying potential.
Eigenvalue distribution of some fractal semi-elliptic differential operators: Combinatorial approach
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