Related papers: Electromagnetic Stekloff eigenvalues: approximatio…

We numerically investigate the generalized Steklov problem for the modified Helmholtz equation and focus on the relation between its spectrum and the geometric structure of the domain. We address three distinct aspects: (i) the asymptotic…

This paper is about the general truncated matrix-valued moment problem. Let $\mathcal{H}_q$ denote the complex Hermitian $q\times q$-matrices, $q\in \mathbb{N}$. Suppose that $(\mathcal{X},\mathfrak{X})$ is a measurable space and…

Motivated by Barr{\'\i}a-Halmos's \cite[Question 19]{barria1982asymptotic} and Halmos's \cite[Problem 237]{Halmos1978A}, we explore projections in Toeplitz algebra on the Hardy space. We show that the product of two Toeplitz (Hankel)…

In this paper we consider the problem of the existence of higher derivatives of the function $t\mapsto\f(A+tK)$, where $\f$ is a function on the real line, $A$ is a self-adjoint operator, and $K$ is a bounded self-adjoint operator. We…

We study concentration operators associated with either the discrete or the continuous Fourier transform, that is, operators that incorporate a spatial cut-off and a subsequent frequency cut-off to the Fourier inversion formula. Their…

We discuss two approaches to solving the parametric (or stochastic) eigenvalue problem. One of them uses a Taylor expansion and the other a Chebyshev expansion. The parametric eigenvalue problem assumes that the matrix $A$ depends on a…

This paper deals with the generalized spectrum of continuously invertible linear operators defined on infinite dimensional Hilbert spaces. More precisely, we consider two bounded, coercive, and self-adjoint operators $\bc{A, B}: V\mapsto…

In this paper we consider eigenvalues asymptotics of the energy operator in the one of the most interesting models of quantum physics, describing an interaction between two-level system and harmonic oscillator. The energy operator of this…

Within the framework of quantum harmonic analysis, for a locally compact group $G$ with a square-integrable, irreducible unitary representation, we analyze the eigenvalue distributions of convolutions between indicator functions on $G$ and…

Analytical solutions are presented for eigenvalues, eigenfunctions of {\color{red} D-dimensional Schrodinger equation having Eckart potential} within Nikiforov-Uvarov method. This uses a new, improved approximation for centrifugal term,…

Contractive selfadjoint extensions of a Hermitian contraction $B$ in a Hilbert space ${\mathfrak H}$ with an exit in some larger Hilbert space ${\mathfrak H}\oplus{\mathcal H}$ are investigated. This leads to a new geometric approach for…

M.Levitin and E.Shargorodsky purposed in a recent article, [math.SP/0212087], the use of the so called ``second order relative spectrum'', to find eigenvalues of self-adjoint operators in gaps of the essential spectrum. Let $M$ be a…

The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…

This paper investigates the asymptotic behavior of the eigenvalues of the biharmonic operator on a thin set with Steklov boundary condition. The thin set is taken to be a tubular neighborhood of a planar smooth domain. We show that, as the…

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence…

In this manuscript, we investigate a priori estimates for the solution to the Dirichlet eigenvalue problem for a broad class of concave elliptic Hessian operators of the form \[ F(D^2u)=-\Lambda u \quad \textrm{in} \, \Omega, \qquad u=0…

We introduce a new method to prove lower estimates for the approximation error of general linear operators with smooth range in terms of classical moduli of smoothness and related $K$-functionals. In addition, we explicitly show how to…

We establish the convergence of a class of numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator. The algorithms act on data…

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…

We establish sufficiency conditions in order to achieve approximation to discrete eigenvalues of self-adjoint operators in the second-order projection method suggested recently by Levitin and Shargorodsky, [math.SP/0212087]. We find…