Quasi Boundary Triples, Self-adjoint Extensions, and Robin Laplacians on the Half-space

Abstract

In this note self-adjoint extensions of symmetric operators are investigated by using the abstract technique of quasi boundary triples and their Weyl functions. The main result is an extension of [5, Theorem 2.6] which provides sufficient conditions on the parameter in the boundary space to induce self-adjoint realizations. As an example self-adjoint Robin Laplacians on the half-space with boundary conditions involving an unbounded coefficient are considered. Quasi boundary triples and self-adjoint extensions

Absence of eigenvalues of non‐self‐adjoint Robin Laplacians on the half‐space

“…Proof. Even though the proof of this result follows a standard scheme (see, for example, [26] or [27]), we will provide it for the sake of completeness (see also [5,Remark 7.5 ii)] and [6,Theorem 3.5] for the proof of a slightly more general result in the case of bounded domains performed using the technique of boundary triples).…”

Absence of eigenvalues of non-self-adjoint Robin Laplacians on the half-space

“…Even though the proof of this result follows a standard scheme (see, e.g., [26] or [28]), we will provide it for the sake of completeness (see also [5,Rem. 7.5 ii)] and [6,Thm. 3.5] for the proof of a slightly more general result in the case of bounded domains performed using the technique of boundary triples).…”

Extensions of derivations and symmetric operators

“…We refer to the references and historical notes in the article [17] by Wegner, the two monographs mentioned above, and also to the monograph of Behrndt, Hassi and de Snoo [6], where extension results are part of an elaborate theory (cf. [6,Corollary 2.1.4.5], and we refer also to the articles of Behrndt-Langer [4] and Behrndt-Schlosser [5]. In a previous article [2], the present authors studied extensions of derivations in a quite different spirit, the main motivation being non-autonomous evolution equations.…”