相关论文: An example of unitary equivalence between self-adj…

We consider minimal non-negative Jacobi operator with $p\times p-$matrix entries. Using the technique of boundary triplets and the corresponding Weyl functions, we describe the Friedrichs and Krein extensions of the minimal Jacobi operator.…

The aim of this paper is to develop an approach to obtain self-adjoint extensions of symmetric operators acting on anti-dual pairs. The main advantage of such a result is that it can be applied for structures not carrying a Hilbert space…

In this paper we prove and apply a theorem of spectral expansion for Schwartz linear operators which have an S-linearly independent Schwartz eigenfamily. This type of spectral expansion is the analogous of the spectral expansion for…

Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets…

Here we give brief account of hermitian symplectic spaces, showing that they are intimately connected to symmetric as well as self-adjoint extensions of a symmetric operator. Furthermore we find an explicit parameterisation of the Lagrange…

This paper is devoted to self-adjoint cyclically compact operators on Hilbert--Kaplansky module over a ring of bounded measurable functions. The spectral theorem for such a class of operators are given. We apply this result to partial…

A famous theorem due to Weyl and von Neumann asserts that two bounded self-adjoint operators are unitarily equivalent modulo the compacts, if and only if their essential spectrum agree. The above theorem does not hold for unbounded…

In this study, we are concerned with spectral problems of second-order vector dynamic equations with two-point boundary value conditions and mixed derivatives, where the matrix-valued coefficient of the leading term may be singular, and the…

A theorem that is of aid in computing the domain of the adjoint operator is provided. It may serve e.g. as a criterion for selfadjointness of a symmetric operator, for normality of a formally normal operator or for $H$--selfadjointness of…

The goal of the paper is to investigate the dynamics of the eigenvalues of the Sturm-Liouville operator with summable PT-symmetric potential on the finite interval. It turns out that the case of a complex Airy operator presents an exactly…

The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations.…

We study inverse spectral problems for ordinary differential equations with regular singularities on compact star-type graphs when differential equations have different orders on diferent edges. As the main spectral characteristics we…

In this paper, we briefly explain the spectral expansion problem for differential operators defined on the entire real line, generated by a differential expression with periodic, complex-valued coefficients.

In this expository article some spectral properties of self-adjoint differential operators are investigated. The main objective is to illustrate and (partly) review how one can construct domains or potentials such that the essential or…

We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…

The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…

Physical self-adjoint extensions and their spectra of the simplest one-dimensional Hamiltonian operator in which the mass is constant except for a finite jump at one point of the real axis are correctly found. Some self-adjoint extensions…

In this paper we construct the spectral expansion for the non-self-adjoint differential operators generated in the space of vektor functions by the ordinary differential expression of arbitrary order with the periodic matrix coefficients by…

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional nonrelativistic motion of a particle in the potential field $V(x)=g_{1}x^{-1}+g_{2}x^{-2}$. For $g_{2}>0$ and $g_{1}<0$, the potential is known as the…

The $J$-matrix method is extended to difference and $q$-difference operators and is applied to several explicit differential, difference, $q$-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures…