9 citations · 22 across the 7 of their papers we have counts for
7 papers
Entire functions in weighted and zero modes of the Pauli operator with non-signdefinite magnetic field
G. Rozenblum, N. Shirokov
For a real non-signdefinite function , $z\in \C$, we investigate the dimension of the space of entire analytical functions square integrable with weight , where t…
Finite Rank Toeplitz Operators: Some Extensions of D.Luecking's Theorem
Alexey Alexandrov, Grigori Rozenblum
The recent theorem by D.Luecking about finite rank Bergman-Toeplitz operators is extended to weights being distributions with compact support and to the spaces of harmonic function…
Counting Schrödinger boundstates: semiclassics and beyond
G. Rozenblum, M. Solomyak
This is a survey of the basic results on the behavior of the number of the eigenvalues of a Schrödinger operator, lying below its essential spectrum. We discuss both fast decaying…
Finite rank Bergman-Toeplitz and Bargmann-Toeplitz operators in many dimensions
Grigori Rozenblum, Nikolay Shirokov
The recent theorem by D. Luecking that finite rank Toeplitz-Bergman operators must be generated by a measure consisting of finitely many point masses is carried over to the many-di…
Discrete spectrum distribution of the Landau Operator Perturbed by an Expanding Electric Potential
Grigori Rozenblum, Alexander V. Sobolev
Under a perturbation by a decaying electric potential, the Landau Hamiltonian acquires some discrete eigenvalues between the Landau levels. We study the perturbation by an "expandi…
Eigenvalue clusters of the Landau Hamiltonian in the exterior of a compact domain
Alexander Pushnitski, Grigori Rozenblum
We consider the Schrodinger operator with a constant magnetic field in the exterior of a compact domain on the plane. The spectrum of this operator consists of clusters of eigenval…