Related papers: Spectral shift for relative Schatten class perturb…

We investigate trace formulas for one-dimensional Schroedinger operators which are trace class perturbations of quasi-periodic finite-gap operators using Krein's spectral shift theory. In particular, we establish the conserved quantities…

We study spectral properties of the Carleman operator (the Hankel operator with kernel $h_{0}(t)=t^{-1}$) and, in particular, find an explicit formula for its resolvent. Then we consider perturbations of the Carleman operator $H_{0}$ by…

This is our third work on Bergman-type operator over bounded domains. In the previous two articles, we systematically study the boundedness, compactness and Schatten membership of Bergman-type on the Hilbert unit ball. In the present paper,…

The aim of this paper is to extend the notion of the spectral order for finite families of pairwise commuting bounded and unbounded selfadjoint operators in Hilbert space. It is shown that the multidimensional spectral order $\preccurlyeq$…

We formulate a variant of Fourier restriction for operators in Schatten classes, where the Fourier-Wigner transform of a bounded operator replaces the Fourier transform of a function. The Fourier-Wigner transform is closely related to the…

We consider a second order self-adjoint operator in a domain which can be bounded or unbounded. The boundary is partitioned into two parts with Dirichlet boundary condition on one of them, and Neumann condition on the other. We assume that…

Let $\mathcal{H}$ be a right quaternionic Hilbert space and let $T$ be a bounded normal right quaternionic linear operator on $\mathcal{H}$. In this paper, we prove that there exists a unique spectral measure $E$ in $\mathcal{H}$ such that…

We build a combinatorial invariant, called the spectral monodromy from the spectrum of a non-selfadjoint h -pseudodifferential operator with two degrees of freedom in the semi-classical limit. We treat small non-selfadjoint perturbation of…

Let $(X,h)$ be a compact and irreducible Hermitian complex space of complex dimension $v>1$. In this paper we show that the Friedrichs extension of both the Laplace-Beltrami operator and the Hodge-Kodaira Laplacian acting on functions has…

We generalise the result of Berger and Shaw the trace formula for Hardy Hilbert space to a larger class of rotation invariant Hilbert function spaces on the unit disk. We also demonstrate many meaningful examples of these Hilbert spaces by…

We study spectral properties of convolution operators $\mathcal L$ and their perturbations $H=\mathcal L+v(x)$ by compactly supported potentials. Results are applied to determine the front propagation of a population density governed by…

We study generalised magnetic Schroedinger operators of the form H(A,V)=h(P^A)+V, where h is an elliptic symbol, P^A is the generator of the magnetic translations, with A a vector potential defining a variable magnetic field B, and V is a…

In this article, we prove the Weyl-von Neumann theorem for antilinear skew-self-adjoint operators. More specifically, we prove the following: Let $A$ be an antilinear skew-self-adjoint operator on a separable Hilbert space $H$ whose kernel…

We study various spectral theoretic aspects of non-self-adjoint operators. Specifically, we consider a class of factorable non-self-adjoint perturbations of a given unperturbed non-self-adjoint operator and provide an in-depth study of a…

In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.

The goal of this paper is the spectral analysis of the Schr\"{o}dinger operator $H=L+V$ , the perturbation of the Taibleson-Vladimirov multiplier $L=\mathcal{D}^{\alpha}$ by a potential $V$. Assuming that $V$ belonges to a class of fast…

Let $a(x,\xi)$ be a real H\"ormander symbol of the type $S_{0,0}^0(\mathbb{R}^{d}\times \mathbb{R}^d)$, let $F$ be a smooth function with all its derivatives globally bounded, and let $K_\delta$ be the self-adjoint Weyl quantization of the…

In this paper, we consider an unbounded selfadjoint operator $A$ and its selfadjoint perturbations in the same Hilbert space $\mathcal{H}$. As S.Albeverio and P. Kurosov (2000), we call a selfadjoint operator $A_{1}$ the singular…

The goal of this paper is twofold. We prove that the operator $H=L+V$ , a perturbation of the Taibleson-Vladimirov multiplier $L=\mathfrak{D}^{\alpha}$ by a potential $V(x)=b\left\Vert x\right\Vert ^{-\alpha},$ $b\geq b_{\ast},$ is…

We study the Koplienko Spectral Shift Function (KoSSF), which is distinct from the one of Krein (KrSSF). KoSSF is defined for pairs $A,B$ with $(A-B)\in\calI_2$, the Hilbert-Schmidt operators, while KrSSF is defined for pairs $A,B$ with…