Related papers: Self-adjoint boundary conditions for the prolate s…
Given a symmetric, semi-bounded, second order elliptic differential operator on a bounded domain with $C^{1,1}$ boundary, we provide a Krein-type formula for the resolvent difference between its Friedrichs extension and an arbitrary…
We study the behaviour of functions of pairs of commuting self-adjoint operators under perturbations by relatively bounded operators. We obtain analogs of our earlier results for functions of a single self-adjoint operator under relatively…
It is useful to have canonical forms of boundary conditions in the study of the eigenvalues of boundary value problems and associated numerical applications. In [J. Appl. Anal. Comput., 2024, 14(4), {1854--1868}], a canonical form is given…
We study the Laplacian in a smooth bounded domain, with a varying Robin boundary condition singular at one point. The associated quadratic form is not semi-bounded from below, and the corresponding Laplacian is not self-adjoint, it has the…
We develop the machinery of boundary triplets for one-dimensional operators generated by formally self-adjoint quasi-differential expression of arbitrary order on a finite interval. The technique are then used to describe all maximal…
We consider the hamiltonian operator associated with planar sec- tions of infinitely long cylindrical solenoids and with a homogeneous magnetic field in their interior. First, in the Sobolev space $\mathcal H^2$, we characterize all…
We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity…
We study a family of differential operators $L_\alpha$ in two variables, depending on the coupling parameter $\alpha\ge0$ that appears only in the boundary conditions. Our main concern is the spectral properties of $L_\alpha$, which turn…
We consider Dirac-type operators on manifolds with boundary, and set out to determine all local smooth boundary conditions that give rise to (strongly) regular self-adjoint operators. By combining the general theory of boundary value…
We investigate the self-adjointness of the two dimensional Dirac operator with infinite mass boundary conditions on an unbounded domain with an infinite number of corners. We prove that if the domain has no concave corners, then the…
In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then using these…
We study the selfadjoint extensions of the spatial part of the D'Alembert operator in a spacetime with two changes of signature. We identify a set of boundary conditions, parametrised by U(2) matrices, which correspond to Dirichlet boundary…
In this paper we study self-adjoint commuting ordinary differential operators. We find sufficient conditions when an operator of fourth order commuting with an operator of order $4g+2$ is self-adjoint. We introduce an equation on…
We show that the boundary conditions entering in the definition of the self-adjoint operator describing the Laplacian plus a finite number of point interactions are local if and only if the corresponding wave equation has finite speed of…
The spectral problem for self-adjoint extensions is studied using the machinery of boundary triplets. For a class of symmetric operators having Weyl functions of a special type we calculate explicitly the spectral projections in the form of…
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…
For the example of the infinitely deep well potential, we point out some paradoxes which are solved by a careful analysis of what is a truly self-adjoint operator. We then describe the self-adjoint extensions and their spectra for the…
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.
It is established that a PT-symmetric elliptic quadratic differential operator with real spectrum is similar to a self-adjoint operator precisely when the associated fundamental matrix has no Jordan blocks.
This paper deals with the study of the two-dimensional Dirac operatorwith infinite mass boundary condition in a sector. We investigate the question ofself-adjointness depending on the aperture of the sector: when the sector is convexit is…