Related papers: Vigier's theorem for the spectral order and its ap…

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…

We give a proof that in settings where Von Neumann deficiency indices are finite the spectral counting functions of two different self-adjoint extensions of the same symmetric operator differ by a uniformly bounded term (see also…

A short introduction to the use of the spectral theorem for self-adjoint operators in the theory of special functions is given. As the first example, the spectral theorem is applied to Jacobi operators, i.e. tridiagonal operators, on…

In this paper, a spectral theorem is proved for self-adjoint cyclically compact partial integral operators in the space of functions with mixed norm, which is a Kaplansky--Hilbert module. The decomposition through eigenfunctions, integral…

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 $\preccurlyeq$…

The notions of infimum and maximal lower bounds of a set $\mathfrak M$ of bounded self-adjoint operators were mainly studied for a set $\mathfrak M$ of two elements. The present paper deals with more general sets $\mathfrak M$, where it is…

The classical spectral theorem completely describes self-adjoint operators on finite dimensional inner product vector spaces as linear combinations of orthogonal projections onto pairwise orthogonal subspaces. We prove a similar theorem for…

We study the spectral theory of operators, generated as direct sums of self-adjoint extensions of quasi-differential minimal operators on a multi-interval set (self-adjoint vector-operators), acting in a Hilbert space. Spectral theorems for…

A decomposition theorem for self-adjoint operators proved by Riesz and Lorch is extended to normal operators. This extension gives a new proof of the spectral theorem for unbounded normal operators.

Covering ill-posed problems with compact and non-compact operators regarding the degree of ill-posedness is a never ending story written by many authors in the inverse problems literature. This paper tries to add a new narrative and some…

Let $A$ be a self-adjoint operator on a Hilbert space $\fH$. Assume that the spectrum of $A$ consists of two disjoint components $\sigma_0$ and $\sigma_1$. Let $V$ be a bounded operator on $\fH$, off-diagonal and $J$-self-adjoint with…

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…

We provide criteria for self-adjointness and {\tau}-Fredhomness of first and second order differential operators acting on sections of infinite dimensional bundles, whose fibers are modules of finite type over a von Neumann algebra A…

The goal of the paper is to study a topology generated by the star order on von Neumann algebras. In particular, it is proved that the order topology under investigation is finer than $\sigma$-strong* topology. On the other hand, we show…

Let A be a self-adjoint operator on a Hilbert space H. Assume that {\sigma} is an isolated component of the spectrum of A, i.e. dist({\sigma},{\Sigma})=d>0 where {\Sigma}=spec(A)\{\sigma}. Suppose that V is a bounded self-adjoint operator…

The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary…

We construct a functional model for rank one perturbations of compact normal operators acting in a certain Hilbert spaces of entire functions generalizing de Branges spaces. Using this model we study completeness and spectral synthesis…

In (J. Funct. Anal. 257, 1092-1132 (2009)), Dykema and Skripka showed the existence of higher order spectral shift functions when the unperturbed self-adjoint operator is bounded and the perturbations is Hilbert-Schmidt. In this article, we…

By nonstandard analysis, a very short and elementary proof of the Spectral Theorem for unbounded self-adjoint operators is given.

We discuss direct and inverse spectral theory of self-adjoint Sturm-Liouville relations with separated boundary conditions in the left-definite setting. In particular, we develop singular Weyl-Titchmarsh theory for these relations.…