Related papers: Essential Self-Adjointness of Anti-Commutative Ope…
In connection with the Fuglede conjecture, we study the existence of commuting self-adjoint extensions of the partial differential operators on arbitrary, possibly disconnected domains in $\br^d$, the associated unitary group, the spectral…
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…
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…
In this note we prove that the maximally defined operator associated with a class of Dirac-type differential expressions M(Q) is J-self-adjoint with respect to a proper antilinear conjugation J under the general hypothesis that the entries…
Let $A_\N$ be the symmetric operator given by the restriction of $A$ to $\N$, where $A$ is a self-adjoint operator on the Hilbert space $\H$ and $\N$ is a linear dense set which is closed with respect to the graph norm on $D(A)$, the…
In this paper we consider the order-like relation for self-adjoint operators on some Hilbert space. This relation is defined by using Jensen inequality. We will show that under some assumptions this relation is antisymmetric.
The purpose of this paper is to make an explicit construction of specific self-adjoint extensions of the Dirac Hamiltonian in the presence of a $\delta$-sphere interaction of finite radius. The exact resolvent kernel of the free Dirac…
In this paper we introduce and study generally non-self-adjoint realizations of the Dirac operator on an arbitrary finite metric graph. Employing the robust boundary triple framework, we derive, in particular, a variant of the Birman…
A new construction for the form sum of positive, selfadjoint operators is given in this paper. The situation is a bit more general, because our aim is to add positive, symmetric operators. With the help of the used method, some commutation…
Given a unitary representation of a Lie group $G$ on a Hilbert space $\mathcal{H}$, we develop the theory of $G$-invariant self-adjoint extensions of symmetric operators both using von Neumann's theorem and the theory of quadratic forms. We…
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 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…
Distinguished selfadjoint extensions of Dirac operators are constructed for a class of potentials including Coulombic ones up to the critical case, $-|x|^{-1}$. The method uses Hardy-Dirac inequalities and quadratic form techniques.
The abstract theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic operator on $\mathbb{R}^{n}$ with linear boundary conditions on (a relatively open part of) a…
We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain…
We prove some Hardy-Dirac inequalities with two different weights including measure valued and Coulombic ones. Those inequalities are used to construct distinguished self-adjoint extensions of Dirac operators for a class of diagonal…
The purpose of this paper is to study nonnegative self-adjoint extensions associated with singular Sturm-Liouville expressions with strictly positive minimal operators. We provide a full characterization of all possible nonnegative…
Devinatz, Nussbaum and von Neumann established some important results on the strong commutativity of self-adjoint and normal unbounded operators. In this paper, we prove results in the same spirit.
The work is devoted to the study of the similarity of a correct restriction to some self-adjoint operator in the case when the minimal operator is symmetric. The resulting theorem was applied to the Sturm-Liouville operator and the Laplace…
In this work we construct self-adjoint extensions of the Dirac operator associated to Hermitian matrix potentials with Coulomb decay and prove that the domain is maximal. The result is obtained by means of a Hardy-Dirac type inequality. In…