Related papers: Irregular and multi--channel sampling of operators
This article proposed a new approach to the determination of the spectrum for nonlinear continuous operators in the Banach spaces and using it investigated the spectrum of some classes of operators. Here shows that in nonlinear operators…
The classical Kramer sampling theorem establishes general conditions that allow the reconstruction of functions by mean of orthogonal sampling formulae. One major task in sampling theory is to find concrete, non trivial realizations of this…
Weighted average sampling is more practical and numerically more stable than sampling at single points as in the classical Shannon sampling framework. Using the frame theory, one can completely reconstruct a bandlimited function from its…
We relate dual-band general Toeplitz operators to block truncated Toeplitz operators and, via equivalence after extension, with Toeplitz operators with $4 \times 4$ matrix symbols. We discuss their norm, their kernel, Fredhomlness,…
In this paper we investigate the spectral and the scattering theory of Schr\"odinger operators acting on perturbed periodic discrete graphs. The perturbations considered are of two types: either a multiplication operator by a short-range or…
We consider Schr\"odinger operators in $\ell^2(\mathbb{Z})$ whose potentials are given by independent (not necessarily identically distributed) random variables. We ask whether it is true that almost surely its spectrum contains an…
Schr\"odinger operators with periodic (possibly complex-valued) potentials and discrete periodic operators (possibly with complex-valued entries) are considered, and in both cases the computational spectral problem is investigated: namely,…
In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory, and from subband filter operators in signal processing.
Let $A,$ $T$ and $B$ be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences $\left\{ A^{n}TB^{n}\right\} $ and…
In the present article, we study the discrete spectrum of certain bounded Toeplitz operators with harmonic symbol on a Bergman space. Using the methods of classical perturbaton theory and recent results by Borichev-Golinskii-Kupin and…
This study is devoted to the asymptotic spectral analysis of multiscale Schr\"odinger operators with oscillating and decaying electric potentials. Different regimes, related to scaling considerations, are distinguished. By means of a normal…
In this article, we characterize absolutely norm attaining normal operators in terms of the essential spectrum. Later we prove a structure theorem for hyponormal absolutely norm attaining (or $\mathcal{AN}$-operators in short) and deduce…
Two variants of generalizations of Hankel operators to the case of linearly ordered abelian groups are considered, criteria of the boundedness and compactness of these operators are given, among them in terms of functions of bounded mean…
This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for…
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate…
In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.
A quasi-product on the normed space is defined. In addition, the notions of the eigenvectors of a linear operator can be extended for the nonlinear operator. Based on the quasi-product and the generalized eigenvectors, the spectral theorems…
This paper establishes an aspect of Bohr's correspondence principle, i.e. that quantum mechanics converges in the high frequency limit to classical mechanics, for commuting semiclassical unitary operators. We prove, under minimal…
A generalized quantum distribution function is introduced. The corresponding ordering rule for non-commuting operators is given in terms of a single parameter. The origin of this parameter is in the extended canonical transformations that…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…