Related papers: Resolvent expansions for self-adjoint operators vi…
For a purely imaginary sign-definite perturbation of a self-adjoint operator, we obtain exponential representations for the perturbation determinant in both upper and lower half-planes and derive respective trace formulas.
In this paper, we investigate the spectrum of the self adjoint differential operator with operator coefficitent in a separable Hilbert space. We also derive asymptotic formulas for the sum of eigenvalues of this operator.
The Grushin plane serves as one of the simplest examples of a sub-Riemannian manifold whose distribution is of non-constant rank. Despite the fact that the singular set where this distribution drops rank is itself a smoothly embedded…
We study the trace class perturbations of the whole-line, discrete Laplacian and obtain a new bound for the perturbation determinant of the corresponding non-self-adjoint Jacobi operator. Based on this bound, we refine the Lieb--Thirring…
We study self-adjoint extensions of operators which are the product of the multiplication operator by an analytic function and the analytic continuation in a strip. We compute the deficiency indices of the product operator for a wide class…
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…
We investigate minimal operator corresponding to operator differential expression with exit from space, study its selfadjoint extensions, also for one particular selfadjoint extension corresponding to boundary value problem with some…
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…
The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations. In the present paper the abstract notion is further developed,…
The problem of variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The aim is to find the best possible upper bound on the norm of the difference of two spectral…
In the terms of triples $D^+\to H\to D^-$ of Hilbert spaces we construct an analogue of Friedrichs's extension for operator matrices. Also we establish some general approach to construction of variational principles for such matrices.
We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…
We study spectral asymptotics for small non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part possesses several invariant Lagrangian tori…
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…
We study Laplace-type operators on hybrid manifolds, i.e. on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace-Beltrami operators on each…
We propose new methods for calculation of the discrete spectrum, the reflection amplitude and the correlation functions of boundary Liouville theory on a strip with Lorentzian signature. They are based on the structure of the vertex…
This article deals with the multidimensional Borg-Levinson theorem for perturbed bi-harmonic operator. More precisely, in a bounded smooth domain of $\R^n$, with $n \geq 2$, we prove the stability of the first and zero order coefficients of…
We derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the Kre{\u\i}n-Vi\v{s}ik-Birman extension scheme, or…
The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…
In this article we are interested for the numerical computation of spectra of non-self adjoint quadratic operators, in two and three spatial dimensions. Indeed, in the multidimensional case very few results are known on the location of the…