Related papers: On spectra of Hankel operators on the polydisc

We characterize the membership of Hankel operators with general symbols in the Schatten Classes $S^p,\, p\in(0,1),$ of the large Bergman spaces $A^2_{\omega}$. The case $p\geq 1$ was proved by Lin and Rochberg.

For a second order operator on a compact manifold satisfying the strong H\"ormander condition, we give a bound for the spectral gap analogous to the Lichnerowicz estimate for the Laplacian of a Riemannian manifold. We consider a wide class…

Let H^2(D) denote the classical Hardy space of the open unit disk D in the complex plane. We obtain descriptions of both the spectrum and essential spectrum of composition operators on H^2(D) whose symbols belong to the class S(2)…

We propose to build a combinatorial invariant, called the spectral monodromy, from the spectrum of a single non-selfadjoint h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from…

We use symbolic expressions for traces of positive integer powers of a Hermitian operator (or, equivalently, coefficients of corresponding characteristic polynomial) to find solutions for the problems as follows: Factorization of…

A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral…

The first step in the counting operator analysis of the spectrum of any model Hamiltonian H is the choice of a Hermitean operator M in such a way that the third commutator with H is proportional to the first commutator. Next one calculates…

Let $\Omega$ be an arbitrary bounded semi-Reinhardt domain in $\mathbb{C}^{m+n}$. We show that for $m \geq 2$, if a Hankel operator with an anti-holomorphic symbol is Hilbert-Schmidt on the Bergman space $L_a^2(\Omega)$, then it must equal…

We consider a polyharmonic operator $H=(-\Delta)^l+V(x)$ in dimension two with $l\geq 6$ and a limit-periodic potential $V(x)$. We prove that the spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at…

Let $m \geq 1$ be an integer and let $H_m(\mathbb B)$ be the analytic functional Hilbert space on the unit ball $\mathbb B \subset \mathbb C^n$ given by the reproducing kernel $K_m(z,w) = (1 - \langle z,w \rangle)^{-m}$. We prove that…

A model operator $H$ associated to a system describing four particles in interaction, without conservation of the number of particles, is considered. We describe the essential spectrum of $H$ by the spectrum of the channel operators and…

The main purpose of this paper is to determine the fine spectrum with respect to Goldberg's classification of the difference operator over the sequence space h. As a new development, we give the approximate point spectrum, defect spectrum…

The paper determines and classifies the spectrum of a non-self-adjoint operator pencil generated by the time-harmonic Maxwell problem with a nonlinear dependence on the frequency for the case of two homogeneous materials joined at a planar…

This paper proves a genericity conjecture by Goldstein, Schlag, and Voda[Invent. Math.\textbf{217}(2019)] for multi-frequency quasiperiodic Schr\"{o}dinger operators. Specifically, we show that for almost all coefficients of real…

We prove a Hankel-variant commutant lifting theorem. This also uncovers the complete structure of the Beurling-type reducing and invariant subspaces of Hankel operators. Kernel spaces of Hankel operators play a key role in the analysis.

We develop the spectral and scattering theory for self-adjoint Hankel operators $H$ with piecewise continuous symbols. In this case every jump of the symbol gives rise to a band of the absolutely continuous spectrum of $H$. We construct…

In this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those…

Let $\Omega\subset \mathbb{C}^2$ be a bounded pseudoconvex complete Reinhardt domain with a smooth boundary. We study the behavior of analytic structure in the boundary of $\Omega$ and obtain a compactness result for Hankel operators on the…

Using an integral formula on a homogeneous Siegel domain, we show a necessary and sufficient condition for composition operators on the weighted Bergman space of a minimal bounded homogeneous domain to be compact. To describe the…

We investigate a type of Hermite orthogonal polynomials on $r$ lines in the plane which have a common point at the origin and endpoints at the $r$ roots of unity and we show that their related Hermite functions are eigenfunctions of a…