arXiv subjects

Rostyslav Kozhan

Publications and source records attributed to Rostyslav Kozhan.

26 records · Page 2Linked to original sources

arXiv2016

Finite range perturbations of finite gap Jacobi and CMV operators

Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range perturbation of a Jacobi or CMV operator from a finite gap isospectral torus. The special case of eventually periodic operators solves an open problem of Simon [25, D.2.7]. We also solve the inverse resonance problem: it is shown that an operator is completely determined by the set of its eigenvalues and resonances, and we provide necessary and sufficient conditions on their configuration for such an operator to exist.

math-ph↗

arXiv2015

Rank one non-Hermitian perturbations of Hermitian $β$-ensembles

For any $β>0$, we provide a tridiagonal matrix model and compute the joint eigenvalue density of a random rank one non-Hermitian perturbation of Gaussian and Laguerre $β$-ensembles of random matrices.

math.PR↗

arXiv2014

Spectral and resonance problem for perturbations of periodic Jacobi operators

Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range or exponentially decaying perturbation of a periodic Jacobi operator. As a corollary we can fully solve the inverse resonance problem: given resonances and eigenvalues we can recover the spectral measure of the Jacobi operator; we provide necessary and sufficient conditions under which such an operator exists and is unique; and we show that the inverse resonance problem is stable under small perturbations.

math.CA↗

arXiv2013

Meromorphic continuations of finite gap Herglotz functions and periodic Jacobi matrices

We find a necessary and sufficient condition for a Herglotz function $m$ to be the Borel transform of the spectral measure of an exponentially decaying perturbation of a periodic Jacobi matrix. The condition is in terms of meromorphic continuation of $m$ to a natural Riemann surface and the structure of its zeros and poles. The analogous result is also established for the Borel transform of the spectral measure of eventually periodic Jacobi matrices. This paper generalizes the corresponding result from [17] for exponentially decaying perturbations of the free Jacobi matrix.

math.SP↗

arXiv2012

L1-spectrum of Banach space valued Ornstein-Uhlenbeck operators

We characterize the $L^1(E;μ_\infty)$-spectrum of the Ornstein-Uhlenbeck operator, where $μ_\infty$ is the invariant measure for the Ornstein-Uhlenbeck semigroup. The main result covers the general case of an infinite-dimensional Banach space E under the assumption that the point spectrum of drift operator $A^*$ is nonempty. This extends several recent related results.

math.CA↗

arXiv2012

Asymptotics of the Eigenvalues of Two-Diagonal Jacobi Matrices

We compute the asymptotics of eigenvalues of Jacobi matrices with the zero coefficients on the main diagonal and the off-diagonal coefficients which converge to zero.

math.SP↗

arXiv2009

Equivalence classes of block Jacobi matrices

The paper contains two results on the equivalence classes of block Jacobi matrices: first, that the Jacobi matrix of type 2 in the Nevai class has A_n coefficients converging to 1, and second, that under an L1-type condition on the Jacobi coefficients, equivalent Jacobi matrices of type 1, 2 and 3 are pairwise asymptotic.

math.SP↗

arXiv2009

Szego asymptotics for matrix-valued measures with countably many bound states

Let $μ$ be a matrix-valued measure with the essential spectrum a single interval and countably many point masses outside of it. Under the assumption that the absolutely continuous part of $μ$ satisfies Szego's condition and the point masses satisfy a Blaschke-type condition, we obtain the asymptotic behavior of the orthonormal polynomials on and off the support of the measure. The result generalizes the scalar analogue of Peherstorfer-Yuditskii and the matrix-valued result of Aptekarev-Nikishin, which handles only a finite number of mass points.

math.SP↗