Quasi boundary triples, self-adjoint extensions, and Robin Laplacians on the half-space

TL;DR

This paper explores self-adjoint extensions of symmetric operators using quasi boundary triples, extending existing theorems, and applies the theory to Robin Laplacians on the half-space with unbounded boundary coefficients.

Contribution

It extends the theory of self-adjoint extensions via quasi boundary triples and provides new conditions for boundary parameters to ensure self-adjointness, with applications to Robin Laplacians.

Findings

Extended Theorem 2.6 to broader boundary parameters.

Provided conditions for self-adjoint Robin Laplacians with unbounded coefficients.

Illustrated the theory with specific boundary value problems.

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 Theorem 2.6 in [5] 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.