Related papers: On the discrete spectrum of non-analytic matrix-va…

An operator matrix $H$ associated with a lattice system describing three particles in interactions, without conservation of the number of particles, is considered. The structure of the essential spectrum of $H$ is described by the spectra…

This paper is concerned with the characterizations of the Friedrichs extension for a class of singular discrete linear Hamiltonian systems. The existence of recessive solutions and the existence of the Friedrichs extension are proved under…

In this paper, we present some checkable criteria for the spectral finiteness of a finite subset of the real $d\times d$ matrix space $\mathbb{R}^{d\times d}$, where $2\le d<\infty$.

In this paper, we consider a parametric hidden Markov model where the hidden state space is non necessarily finite. We provide a necessary and sufficient condition for the invertibility of the limiting Fisher information matrix.

In the paper, a simple condition guaranteing the finiteness property for a bounded set of matrices is presented. Given a bounded set S of real or complex matrices, it is shown that existence of a sequence of matrix products such that the…

The Friedrichs extension of minimal linear relation being bounded below and associated with the discrete symplectic system with a special linear dependence on the spectral parameter is characterized by using recessive solutions. This…

Sufficient conditions for a discrete spectrum of the biharmonic equation in a two-dimensional peak-shaped domain are established. Different boundary conditions from Kirchhoff's plate theory are imposed on the boundary and the results depend…

We consider some compact non-selfadjoint perturbations of fibered one-dimensional discrete Schr\"odinger operators. We show that the perturbed operator exhibits finite discrete spectrum under suitable\- regularity conditions.

In this short paper we show that March's criterion for the existence of a bounded non constant harmonic function on a weak model is also a necessary and sufficient condition for the solvability of the Dirichlet problem at infinity on a…

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 use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…

We extend the notions of "$R_\infty$-property" and "full (extended) Reidemeister spectrum" to finite groups in a meaningful way. We provide examples of finite groups admitting these properties, if they exist, by looking at groups of small…

Using graph-theoretic techniques for f.g. subgroups of $F^{\mathbb{Z}[t]}$ we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked…

Let H=$\Delta +V$ be a Schr\"odinger on a complete non-compact manifold. It is known since the work of Fischer-Colbrie and Schoen that the finiteness of the negative spectrum of $H$ implies the existence of a function $\phi$ solution of…

We consider the spectrum of the discrete Schr\"odinger equation with one-dimensional perturbation. We obtain the explicit form of scattering matrix and find the exact condition of absence of singular part of the spectrum. We calculated also…

We develop a max-plus spectral theory for infinite matrices. We introduce recurrence and tightness conditions, under which many results of the finite dimensional theory, concerning the representation of eigenvectors and the asymptotic…

We discuss a functional model for multi--diagonal selfadjoint operators with almost periodic coefficients that generalizes the well known model for finite band Jacobi matrices. It give us an opportunity to construct examples of almost…

We prove that the finiteness of a finitely generated category of irreducible algebraic varieties over a field of characteristic zero is decidable. We also obtain a Burnside finiteness criterion for such a category, with applications to…

It is proven that the absolutely continuous spectrum of matrix Schr\"{o}dinger operators coincides (with the multiplicity taken into account) with the spectrum of the unperturbed operator if the (matrix) potential is square integrable. The…

We prove that if f is a self-map of an algebraic variety over a field K, then under certain conditions on X, f and K the set of possible periods of K-valued periodic points of f is finite.