Related papers: The complex Airy operator with a semi-permeable ba…

We consider a polyharmonic operator $H=(-\Delta)^l+V(\x)$ in dimension two with $l\geq 2$, $l$ being an integer, and a quasi-periodic potential $V(\x)$. We prove that the absolutely continuous spectrum of $H$ contains a semiaxis and there…

We provide a detailed description of the model Hilbert space $L^2(\bbR; d\Sigma; \cK)$, were $\cK$ represents a complex, separable Hilbert space, and $\Sigma$ denotes a bounded operator-valued measure. In particular, we show that several…

In this note, it is shown that the stochastic Airy operator, which is the "Schr\"odinger operator" on the half-line whose potential term consists of Gaussian white noise plus a linear term tending to $+\infty$, can naturally be defined as a…

We analyze the spectrum of the operator $\Delta^{-1} [\nabla \cdot (K\nabla u)]$, where $\Delta$ denotes the Laplacian and $K=K(x,y)$ is a symmetric tensor. Our main result shows that this spectrum can be derived from the spectral…

We introduce a simple, general, and convergent scheme to compute generalized eigenfunctions of self-adjoint operators with continuous spectra on rigged Hilbert spaces. Our approach does not require prior knowledge about the eigenfunctions,…

In the first part of the paper we show Weyl type spectral asymptotic formulas for pseudodifferential operators $P_a$ of order $2a$, with type and factorization index $a\in R_+$, restricted to compact sets with boundary; this includes…

In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of…

Bounded composition operators in Paley-Wiener spaces have simple forms, and they are just operators composed through affine mappings of the complex plane. The purpose of this article is to explore some notions about bounded operators and…

In this paper we examine the asymptotic structure of the pseudospectrum of the singular Sturm-Liouville operator $L=\partial_x(f\partial_x)+\partial_x$ subject to periodic boundary conditions on a symmetric interval, where the coefficient…

This paper presents a groundbreaking advancement in the theory of operators defined on octonionic Hilbert spaces, successfully resolving a fundamental challenge that has persisted for over six decades. Due to the intrinsic non-associative…

We study the Schr\"odinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and…

In this dissertation I establish that a broad class of Banach *-algebras of infinite integral operators, defined by the property that the kernels of the elements of the algebras possess subexponential off-diagonal decay, is inverse closed…

We consider the Schr\"odinger operator $H_{\eta W} = -\Delta + \eta W$, self-adjoint in $L^2({\mathbb R}^d)$, $d \geq 1$. Here $\eta$ is a non constant almost periodic function, while $W$ decays slowly and regularly at infinity. We study…

Using the approach proposed in [5] , in an infinite-dimensional separable complex Hilbert space we give abstract constructions of families $\{{\mathcal T}_z\}_{{\rm Im\,} z>0}$ of closed densely defined symmetric operators with the…

A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen…

The Weyl-Sims classification for a second-order ordinary differential equation with general complex coefficients is investigated. Connections are then established between the associated m-function and the spectral properties of…

In this paper we study the spectrum of a fundamental differential operator on a Hilbert-P\'olya space. A number is an eigenvalue of this differential operator if and only if it is a nontrivial zero of the Riemann zeta function. An explicit…

Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…

This is a short survey on the connection between general extension theories and the study of realizations of elliptic operators A on smooth domains in R^n, n > 1. The theory of pseudodifferential boundary problems has turned out to be very…

In this article, we study the spectrum of the magnetic Dirac operator, and the magnetic Dirac operator with potential over complete Riemannian manifolds. We find sufficient conditions on the potentials as well as the manifold so that the…