Related papers: On the discrete spectrum of complex banded matrice…
The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete laplacian is under consideration. The rate of stabilization for the the matrix entries which provides finiteness of the discrete spectrum and is…
We study spectrum inclusion regions for complex Jacobi matrices which are compact perturbations of real periodic Jacobi matrices. The condition sufficient for the lack of discrete spectrum for such matrices is given
We study spectrum inclusion regions for complex Jacobi matrices which are compact perturbations of the discrete laplacian. The condition sufficient for the lack of discrete spectrum for such matrices is given.
We are interested in the phenomenon of the essential spectrum instability for a class of unbounded (block) Jacobi matrices. We give a series of sufficient conditions for the matrices from certain classes to have a discrete spectrum on a…
In this paper, a new class of band matrices is considered where the entries of each non-zero band form a sequence with two limit points. The compact perturbation technique is used to study the spectrum over the $\ell_{p}, (1<p<\infty)$…
For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end we…
We present pretty detailed spectral analysis of Jacobi matrices with periodically modulated entries in the case when $0$ lies on the soft edge of the spectrum of the corresponding periodic Jacobi matrix. In particular, we show that the…
We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous on some subsets of the complex plane and we provide…
The spectrum of triangular band matrices defined on the sequence spaces where the entries of each band is a constant or convergent sequence is well studied. In this article, the spectrum and fine spectrum of a new generalised difference…
In this note we investigate the discrete spectrum of Jacobi matrix corresponding to polynomials defined by recurrence relations with periodic coefficients. As examples we consider a)the case when period $N$ of coefficients of recurrence…
Recent results of Denisov and Kaluzhny-Shamis describe the absolutely continuous spectrum of Jacobi matrices with coefficients that obey an l^2 bounded variation condition with step p and are asymptotically periodic. We extend these results…
The spectrum of three-diagonal self-adjoint $p$-periodic Jacobi matrix with positive off-diagonal elements $a_n$ an real diagonal elements $b_n$ consist of intervals separated by $p-1$ gaps $\gamma_i$, where some of the gaps can be…
Under the mild trace-norm assumptions we show that the eigenvalues of a generic (non Hermitian) complex perturbation of a Jacobi matrix sequence (not necessarily real) are still distributed as the real-valued function $2\cos t$ on…
We consider the 1D periodic Jacobi matrices. The spectrum of this operator is purely absolutely continuous and consists of intervals separated by gaps. We solve the inverse problem (including characterization) in terms of vertical slits on…
This paper extends our previous works arXiv:1802.07306 [math.NT], arXiv:1808.02382 [math.NT] on determining the spectrum, in the Berkovich sense, of ultrametric linear differential equations. Our previous works focused on equations with…
The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations.…
We obtain the estimate of the Lebesgue measure of the spectrum for the direct integral of matrix-valued functions. These estimates are applicable for a wide class of discrete periodic operators. For example: these results give new and sharp…
We study the spectral properties of bounded and unbounded Jacobi matrices whose entries are bounded operators on a complex Hilbert space. In particular, we formulate conditions assuring that the spectrum of the studied operators is…
In this paper, we investigate the discrete spectrum of probability measures for actions of locally compact groups. We establish that a probability measure has a discrete spectrum if and only if it has bounded measure-max-mean-complexity. As…
We study spectral properties of unbounded Jacobi matrices with periodically modulated or blended entries. Our approach is based on uniform asymptotic analysis of generalized eigenvectors. We determine when the studied operators are…