Related papers: A Collection of Problems on Spectrally Bounded Ope…
In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary differential expression with periodic, complex-valued…
A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem…
This article introduces several new upper bounds for the $q$-numerical radius of bounded linear operators on complex Hilbert spaces. Our results refine some of the existing upper bounds in this field. The $q$-numerical radius inequalities…
In this paper we consider a generalized version of bounded oscillation operators, involving new parameters in the definition, as well as considering the operators on vector-valued function spaces. With this definition we will capture some…
This is a survey of some recent applications of Boolean valued models of set theory to order bounded operators in vector lattices.
We consider selfadjoint operators obtained by pasting a finite number of boundary relations with one-dimensional boundary space. A typical example of such an operator is the Schr\"odinger operator on a star-graph with a finite number of…
We study two classes of bounded operators on mixed norm Lebesgue spaces, namely composition operators and product operators. A complete description of bounded composition operators on mixed norm Lebesgue spaces are given. For a certain…
We review the spectral and the scattering theory for the Aharonov-Bohm model on R^2. New formulae for the wave operators and for the scattering operator are presented. The asymptotics at high and at low energy of the scattering operator are…
We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…
The work is devoted to the study of Laplace operator when the potential is a singular generalized function and plays the role of a singular perturbation of a Laplace operator. Abstract theorem obtained earlier by the authors B.N. Biyarov…
We carry the index theory for manifolds with boundary of B\"ar and Ballmann over to first order differential operators on metric graphs. This approach results in a short proof for the index of such operators. Then the self-adjoint…
In this work, a connection between some spectral properties of direct sum of operators in the direct sum of Hilbert spaces and its coordinate operators has been investigated.
Multiple scalar integral representations for traces of operator derivatives are obtained and applied in the proof of existence of the higher order spectral shift functions.
The research on spectral inequalities for discrete Schrodinger Operators has proved fruitful in the last decade. Indeed, several authors analysed the operator's canonical relation to a tridiagonal Jacobi matrix operator. In this paper, we…
This paper establishes some of the fundamental barriers in the theory of computations and finally settles the long-standing computational spectral problem. That is to determine the existence of algorithms that can compute spectra…
We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…
We study a number of topics in the theory of Boolean Representable Simplicial Complexes (BRSC). These include various operators on BRSC. We look at shellability in higher dimensions and propose a number of new conjectures.
This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…
The class of matrix optimization problems (MOPs) has been recognized in recent years to be a powerful tool by researchers far beyond the optimization community to model many important applications involving structured low rank matrices.…
In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.