Grigori Rozenblioum

Professor Emeritus at Mathematical Sciences

Research interests are concentrated around mathematical problems arising in physics, especially quantum physics, and include Partial Differerential Equations, Operator Theory and Analysis. Program head of the program Hamiltonians with Magnetic Fields at Institut Mittag-Leffler. Member of the editorial board of two journals. Has been teaching at universities in Russia, Denmark and Sweden since 1974.

Source: chalmers.se
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Showing 66 publications

2023

The discrete spectrum of the Neumann-Poincaré operator in 3D elasticity

Grigori Rozenblioum
Journal of Pseudo-Differential Operators and Applications. Vol. 14 (2)
Journal article
2023

Discrete spectrum of zero order pseudodifferential operators.

Grigori Rozenblioum
Opuscula Mathematica. Vol. 43 (2), p. 247-268
Journal article
2023

Weyl asymptotics for Poincaré–Steklov eigenvalues in a domain with Lipschitz boundary

Grigori Rozenblioum
Journal of Spectral Theory. Vol. 13 (3), p. 755-803
Journal article
2023

Spectral theorem approach to commutative C<sup>⁎</sup>-algebras generated by Toeplitz operators on the unit ball: Quasi-elliptic related cases

Grigori Rozenblioum, N. Vasilevski
Journal of Mathematical Analysis and Applications. Vol. 528 (2)
Journal article
2022

Commutative Algebras of Toeplitz Operators on the Bergman Space Revisited: Spectral Theorem Approach

Grigori Rozenblioum, N. Vasilevski
Integral Equations and Operator Theory. Vol. 94 (3)
Journal article
2022

Eigenvalues of the Birman-Schwinger operator for singular measures: The noncritical case

Grigori Rozenblioum, Grigory Tashchiyan
Journal of Functional Analysis. Vol. 283 (12)
Journal article
2022

Spectral Estimates and Asymptotics for Integral Operators on Singular Sets

Grigori Rozenblioum, Grigory Tashchiyan
Journal of Mathematical Sciences. Vol. 268 (4), p. 493-508
Journal article
2022

Eigenvalues of singular measures and Connes’ noncommutative integration

Grigori Rozenblioum
Journal of Spectral Theory. Vol. 12 (1), p. 259-300
Journal article
2022

Eigenvalue asymptotics for polynomially compact pseudodifferential operators.

Grigori Rozenblioum
St. Petersburg Mathematical Journal. Vol. 33 (2), p. 341-353
Journal article
2022

Eigenvalue asymptotics for polynomially compact pseudodifferential operators

Grigori Rozenblioum
St. Petersburg Mathematical Journal. Vol. 33 (2), p. 341-353
Journal article
2022

Lieb–Thirring Estimates for Singular Measures

Grigori Rozenblioum
Annales Henri Poincare. Vol. 23 (11), p. 4130-4115
Journal article
2022

Eigenvalues of singular measures and Connes' noncommutative integration.

Grigori Rozenblioum
Journal of Spectral Theory. Vol. 12 (1), p. 259-300
Journal article
2022

TOPOLOGICAL OBSTRUCTIONS TO THE DIAGONALISATION OF PSEUDODIFFERENTIAL SYSTEMS

Matteo Capoferri, Grigori Rozenblioum, Nikolai Saveliev et al
Proceedings of the American Mathematical Society, Series B. Vol. 9 (43), p. 472-486
Journal article
2021

Eigenvalue Asymptotics for Weighted Polyharmonic Operator with a Singular Measure in the Critical Case

Grigori Rozenblioum, E. M. Shargorodsky
Functional Analysis and its Applications. Vol. 55 (2), p. 170-173
Journal article
2021

Eigenvalue asymptotics for polynomially compact pseudodifferential operators

Grigori Rozenblioum
Algebra i Analiz. Vol. 33 (2), p. 215-233
Journal article
2021

Spectral properties of the Neumann-Poincaré operator in 3D elasticity

Y. Miyanishi, Grigori Rozenblioum
International Mathematics Research Notices. Vol. 2021 (11), p. 8715-8740
Journal article
2021

Eigenvalue estimates and asymptotics for weighted pseudodifferential operators with singular measures in the critical case.

Grigori Rozenblioum, E. M. Shargorodsky
Partial Differential Equations, Spectral Theory, and Mathematical Physics (EMS Series of Congress Reports). Vol. 18, p. 331-354
Paper in proceeding
2020

Toeplitz operators with singular symbols in polyanalytic Bergman spaces on the half-plane

Grigori Rozenblioum, N. Vasilevski
Operator Theory: Advances and Applications. Vol. 279, p. 403-421
Book chapter
2020

EIGENVALUES OF THE NEUMANN-POINCARE OPERATOR IN DIMENSION 3: WEYL'S LAW AND GEOMETRY

Y. Miyanishi, Grigori Rozenblioum
St. Petersburg Mathematical Journal. Vol. 31 (2), p. 371-386
Journal article
2020

Nikolai’s spaces

Grigori Rozenblioum
Operator Theory: Advances and Applications. Vol. 279, p. 25-26
Book chapter
2020

Trace Class Toeplitz Operators with Singular Symbols

Grigori Rozenblioum, Nikolai L. Vasilevski
Proceedings of the Steklov Institute of Mathematics. Vol. 311 (1), p. 225-232
Journal article
2019

Toeplitz operators in polyanalytic bergman type spaces

Grigori Rozenblioum, N. Vasilevski
Contemporary Mathematics. Vol. 733, p. 273-290
Book chapter
2019

L–Invariant Fock–Carleson Type Measures for Derivatives of Order k and the Corresponding Toeplitz Operators

K. Esmeral, Grigori Rozenblioum, N. Vasilevski
Journal of Mathematical Sciences. Vol. 242 (2), p. 337-358
Journal article
2019

On the mathematical work of Mikhail Zakharovich Solomyak

Grigori Rozenblioum
St. Petersburg Mathematical Journal. Vol. 30 (3), p. 391-410
Journal article
2018

Toeplitz operators via sesquilinear forms

Grigori Rozenblioum, N. Vasilevski
Operator Theory: Advances and Applications. Vol. 262, p. 287-304
Book chapter
2018

Eigenvalue asymptotics for potential type operators on lipschitz surfaces of codimension greater than 1

Grigori Rozenblioum, Grigory Tashchiyan
Opuscula Mathematica. Vol. 38 (5), p. 733-758
Journal article
2017

Eigenvalue asymptotics for the sturm-liouville operator with potential having a strong local negative singularity

Medet Nursultanov, Grigori Rozenblioum
Opuscula Mathematica. Vol. 37 (1), p. 109-139
Journal article
2016

Isoperimetric inequalities for Schatten norms of Riesz potentials

Grigori Rozenblioum, M. Ruzhansky, D. Suragan
Journal of Functional Analysis. Vol. 271 (1), p. 224-239
Journal article
2016

Toeplitz Operators in the Herglotz Space

Grigori Rozenblioum, N. Vasilevski
Integral Equations and Operator Theory. Vol. 86 (3), p. 409-438
Journal article
2016

Toeplitz Operators Defined by Sesquilinear Forms: Bergman Space Case

Grigori Rozenblioum, N. Vasilevski
Journal of Mathematical Sciences. Vol. 213 (4), p. 582-609
Journal article
2015

The Finite Rank Theorem for Toeplitz Operators on the Fock Space

A.A. Borichev, Grigori Rozenblioum
Journal of Geometric Analysis. Vol. 25 (1), p. 347-356
Journal article
2014

Some weighted estimates for the ∂̅-equation and a finite rank theorem for Toeplitz operators in the Fock space

Grigori Rozenblioum, Nikolay Shirokov
Proceedings of the London Mathematical Society. Vol. 109 (5), p. 1281-1303
Journal article
2014

On Spectral Estimates for the Schrodinger Operators in Global Dimension 2

Grigori Rozenblioum, M. Solomyak
St. Petersburg Mathematical Journal. Vol. 25 (3), p. 495-505
Journal article
2014

Toeplitz operators defined by sesquilinear forms: Fock space case

Grigori Rozenblioum, N. Vasilevski
Journal of Functional Analysis. Vol. 267 (11), p. 4399-4430
Journal article
2013

On spectral estimates for the Schrödinger operators in global dimension 2

Grigori Rozenblioum, Michail Solomyak
Algebra and Analysis. Vol. 25 (3), p. 185-199
Journal article
2012

Finite rank Bargmann–Toeplitz operators with non-compactly supported symbols

Grigori Rozenblioum
Bulletin of Mathematical Sciences. Vol. 2 (2), p. 331-341
Journal article
2011

On lower eigenvalue bounds for Toeplitz operators with radial symbols in Bergman spaces

Grigori Rozenblioum
Journal of Spectral Theory. Vol. 1 (3), p. 299-325
Journal article
2011

Spectral estimates for Schrödinger operators with sparse potentials on graphs

Grigori Rozenblioum, Michael Solomyak
Journal of Mathematical Sciences. Vol. 176 (3), p. 458-474
Journal article
2011

On the spectrum of Bargmann- Toeplitz operators with symbols of variable sign.

A. Pushnitsky, Grigori Rozenblioum
Journal dAnalyse Mathematique. Vol. 114 (1), p. 317-340
Journal article
2010

Finite Rank Bergman-Toeplitz and Bargmann-Toeplitz Operators in Many Dimensions

Grigori Rozenblioum, Nikolay Shirokov
Complex Analysis and Operator Theory. Vol. 4 (4), p. 767-775
Journal article
2010

On spectral estimates for Schrödinger-type operators: The case of small local dimension

Grigori Rozenblioum, Michael Solomyak
Functional Analysis and its Applications. Vol. 44 (4), p. 259-269
Journal article
2010

Entire Functions in Weighted L2 and Zero Modes of the Pauli Operator with Non-Signdefinite Magnetic Field.

Grigori Rozenblioum, Nikolay Shirokov
CUBO, a mathematical journal. Vol. 12 (1), p. 115-132
Journal article
2009

Finite rank Toeplitz operators: some extensions of D. Luecking's theorem.

Alexei Aleksandrov, Grigori Rozenblioum
Journal of Functional Analysis. Vol. 256 (7), p. 2291-2303
Journal article
2009

A Laplace operator with boundary conditions singular at one point

Marco Marlettta, Grigori Rozenblioum
Journal of Physics A: Mathematical and Theoretical. Vol. 42 (12)
Journal article
2009

Counting Schrödinger boundstates: semiclassics and beyond.

Grigori Rozenblioum, Michael Solomyak
Sobolev spaces in mathematics. Int. Math. Ser. (N. Y.), 9, Springer, New York, 2009.. Vol. II, p. 329-353
Journal article
2009

Finite Rank Toeplitz Operators in the Bergman space

Grigori Rozenblioum
Around the Research of V. Maz'ya. III. International Mathematical Series. Springer.. Vol. 13, p. 331-358
Journal article
2009

On the spectral estimates for the Schrödinger operator on $\Bbb Z^d, d\ge3$

Grigori Rozenblioum
J. Math. Sci. (N. Y.). Vol. 159 (2), p. 241--263-
Journal article
2009

On the Spectral Properties of the Landau Hamiltonian Perturbed by a moderately Decaying Magnetic Field.

Grigori Rozenblioum, Grigory Tashchiyan
Spectral and Scattering Theory for Quantum Magnetic Systems. AMS contemporary Mathematics. Vol. 500
Journal article
2008

On the spectral properties of the perturbed Landau Hamiltonian.

Grigori Rozenblioum, Grigory Tashchiyan
Communications in Partial Differential Equations. Vol. 33 (4-6), p. 1048--1081-1081
Journal article
2008

Counting Sobolev boundstates. Semiclassics and beyond

Grigori Rozenblioum, Mikhail Solomyak
Sobolev Spaces in Mathematics II. Internat. Mathem.Series. Springer. Vol. 9, p. 329-354
Journal article
2008

Eigenvalue analysis of elliptic operators

Grigori Rozenblioum
Topics in Mathematical Analysis, Series on Analysis, Appl. and Comput. World Scientific, p. 227-256
Book chapter
2008

Discrete spectrum distribution of the Landau operator perturbed by an expanding electric potential

Grigori Rozenblioum, Alexander Sobolev
Spectral Theory of Differential Operators: M. Sh. Birman 80th Anniversary Collection. AMS Translations II. Vol. 225, p. 169-190
Journal article
2007

Eigenvalue clusters of the Landau Hamiltonian in the exterior of a compact domain

A. Pushnitski, Grigori Rozenblioum
Documenta Mathematica. Vol. 12, p. 569-586
Journal article
2007

Eigenvalue clusters of the Landau Hamiltonian in the exterior of a compact domain

Grigori Rozenblioum, Alexander Pushnitski
Documenta Mathematica. Vol. 12, p. 569--586-
Journal article
2007

On a family of differential operators with the coupling parameter in the boundary condition.

Grigori Rozenblioum, Mikhail Solomyak
Journal of Computational and Applied Mathematics. Vol. 208 (1), p. 57--71-
Journal article
2006

Eigenvalue Asymptotics for Potential Type Operators on Lipschitz Surfaces

Grigori Rozenblioum, Grigory Tashchiyan
Russian Journal of Mathematical Physics. Vol. 13 (3), p. 326-339
Journal article
2006

Infiniteness of zero modes for the Pauli operator with singular magnetic field

Grigori Rozenblioum, Nikolay Shirokov
Journal of Functional Analysis. Vol. 333 (1), p. 135-172
Journal article
2005

Guillemin transform and Toeplitz representations for operators on singular manifolds.

Grigori Rozenblioum
Spectral geometry of manifolds with boundary and decomposition of manifolds, Contemp. Math., 366, Amer. Math. Soc., Providence, RI, 2005., p. 281--306-
Paper in proceeding
2005

Schrödinger operators with singular potentials.

Grigori Rozenblioum, Michael Melgaard
Handbook of Differential Equations. Stationary partial differential equations. Vol. II, Elsevier, p. 407--517-
Book chapter
2004

Negative discrete spectrum of perturbed multivortex Aharonov-Bohm Hamiltonians.

Grigori Rozenblioum, Michael Melgaard, Grigori Rozenblioum
Annales Henri Poincare. Vol. 5 (5), p. 979--1012-1012
Journal article
2002

Lieb-Thirring inequality for the Aharonov-Bohm Hamiltonian and eigenvalue estimates

Michael Melgaard, E.-M. Ouhabaz, Grigori Rozenblioum
Preprint
2001

Toeplitz representations for operators on singular manifolds

V. Nazaikinskii, Grigori Rozenblioum, B. Sternin
Preprint
1996

The index of cone mellin operator

Grigori Rozenblioum
Preprint

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