Related papers: The singularly continuous spectrum and non-closed …

We study the spectral convergence of compact, self-adjoint operators on a separable Hilbert space under operator norm perturbations, and derive asymptotic expansions for their eigenvalues and eigenprojections. Our analysis focuses on…

We consider a linear symmetric operator in a Hilbert space that is neither bounded from above nor from below, admits a block decomposition corresponding to an orthogonal splitting of the Hilbert space and has a variational gap property…

We study sub-Dirac operators that are associated with left-invariant bracket-generating sub-Riemannian structures on compact quotients of nilpotent semi-direct products $G=\mathbb{R}^n\rtimes_A\mathbb{R}$. We will prove that these operators…

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…

In this paper we study in a Hilbert space a homogeneous linear second order difference equation with nonconstant and noncommuting operator coefficients. We build its exact resolutive formula consisting in the explicit non-iterative…

For a given self-adjoint operator $A$ with discrete spectrum, we completely characterize possible eigenvalues of its rank-one perturbations~$B$ and discuss the inverse problem of reconstructing $B$ from its spectrum.

We study Schr\"{o}dinger operator $H=-\Delta+V(x)$ in dimension two, $V(x)$ being a limit-periodic potential. We prove that the spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this…

We study the solvability complexity index (SCI) for unbounded selfadjoint operators on separable Hilbert spaces and perturbations thereof. In particular, we show that if the extended essential spectrum of a selfadjoint operator is convex,…

We consider a non-self-adjoint $H$ given as the perturbation of a self-adjoint operator $H_0$. We suppose that $H$ is of the form $H=H_0+CWC$ where $C$ is a bounded, positive definite and relatively compact with respect to $H_0$, and $W$ is…

Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show that the spectrum of $A$ decomposes,…

This paper establishes a theory of nonlinear spectral decompositions by considering the eigenvalue problem related to an absolutely one-homogeneous functional in an infinite-dimensional Hilbert space. This approach is both motivated by…

Criteria are formulated both for the existence and for the non-existence of complex eigenvalues for a class of non self-adjoint operators in Hilbert space invarariant under a particular discrete symmetry. Applications to the PT-symmetric…

The main objective of this dissertation is to analyse thoroughly the construction of self-adjoint extensions of the Laplace-Beltrami operator defined on a compact Riemannian manifold with boundary and the role that quadratic forms play to…

Let $H_0$ be a periodic operator on $\R^+$(or periodic Jacobi operator on $\N$). It is known that the absolutely continuous spectrum of $H_0$ is consisted of spectral bands $\cup[\alpha_l,\beta_l]$. Under the assumption that $\limsup_{x\to…

In this paper we solve several problems concerning joint similarity to n-tuples of operators in noncommutative varieties in $[B(\cH)^n]_1$ associated with positive regular free holomorphic functions in $n$ noncommuting variables and with…

We characterize possible spectra of rank-one perturbations B of a self-adjoint operator A with discrete spectrum and, in particular, prove that the spectrum of B may include any number of real or non-real eigenvalues of arbitrary algebraic…

Continuous movement of discrete spectrum of the Schr\"{o}dinger operator $H(z)=-\frac{d^2} {dx^2}+V_0+z V_1$, with $\int_0^\infty {x |V_j(x)| dx} < \infty$, on the half-line is studied as $z$ moves along a continuous path in the complex…

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 prove that given a symmetric completely non-selfadjoint operator $B$ with finite deficiency indices $(n,n)$ on a Hilbert space and a boundary triplet $\left(\mathbb{C}^{n},\Gamma_{1},\Gamma_{2}\right)$ for $B^{*}$, the set of points in…

In this work the spectral theory of self-adjoint operator $A$ represented by Jacobi matrix is considered. The approach is based on the continued fraction representation of the resolvent matrix element of $A$. Different criteria of absolute…