Related papers: Formally self-adjoint quasi-differential operators…

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…

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…

We establish a bijection between the self-adjoint extensions of the Laplace operator on a bounded regular domain and the unitary operators on the boundary. Each unitary encodes a specific relation between the boundary value of the function…

We study two- and three-dimensional matrix Schr\"odinger operators with $m\in \mathbb N$ point interactions. Using the technique of boundary triplets and the corresponding Weyl functions, we complete and generalize the results obtained by…

We produce a simple criterion and a constructive recipe to identify those self-adjoint extensions of a lower semi-bounded symmetric operator on Hilbert space which have the same lower bound as the Friedrichs extension. Applications of this…

We introduce the notion of formally self-adjoint conformally covariant polydifferential operators and give some constructions of families of such operators. In one direction, we show that any homogeneous conformally variational scalar…

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.…

We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…

Using boundary triples, we develop an abstract framework to investigate the complete non-selfadjointness of the maximally dissipative extensions of dissipative operators of the form $S+iV$, where $S$ is symmetric with equal finite defect…

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…

We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…

We use the boundary triplet approach to extend the classical concept of perturbation determinants to a more general setup. In particular, we examine the concept of perturbation determinants to pairs of proper extensions of closed symmetric…

We extend the notion of generalized boundary triples and their Weyl functions from extension theory of symmetric operators to adjoint pairs of operators, and we provide criteria on the boundary parameters to induce closed operators with a…

This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…

The paper considers the general form of self-adjoint boundary value problems for momentum operators with nonlocal potentials. We give an analysis of the eigenvalue distribution as zeros of the characteristic functions, for which their…

We provide a simple recipe for obtaining all self-adjoint extensions, together with their resolvent, of the symmetric operator $S$ obtained by restricting the self-adjoint operator $A:\D(A)\subseteq\H\to\H$ to the dense, closed with respect…

We consider self-adjoint extensions of differential operators of the type $ (-\frac{d^2}{dr^2} + \frac{l(l+1)}{r^2})^3 $ on the real semi-axis for l=1,2 with two kinds of boundary conditions: first that nullify the value of a function and…

We consider the formal prolate spheroid differential operator on a finite symmetric interval and describe all its self-adjoint boundary conditions. Only one of these boundary conditions corresponds to a self-adjoint differential operator…

We consider a class of self-adjoint extensions using the boundary triple technique. Assuming that the associated Weyl function has the special form $M(z)=\big(m(z)\Id-T\big) n(z)^{-1}$ with a bounded self-adjoint operator $T$ and scalar…

In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions…