Selfadjoint extensions of the LaplaceBeltrami operator and unitaries at the boundary
Abstract
We construct in this article a class of closed semibounded quadratic forms on the space of square integrable functions over a smooth Riemannian manifold with smooth boundary. Each of these quadratic forms specifies a semibounded selfadjoint extension of the LaplaceBeltrami operator. These quadratic forms are based on the Lagrange boundary form on the manifold and a family of domains parametrized by a suitable class of unitary operators on the boundary that will be called admissible. The corresponding quadratic forms are semibounded below and closable. Finally, the representing operators correspond to semibounded selfadjoint extensions of the LaplaceBeltrami operator. This family of extensions is compared with results existing in the literature and various examples and applications are discussed.
 Publication:

arXiv eprints
 Pub Date:
 August 2013
 arXiv:
 arXiv:1308.0527
 Bibcode:
 2013arXiv1308.0527I
 Keywords:

 Mathematics  Spectral Theory;
 Mathematical Physics;
 Mathematics  Functional Analysis;
 47B25;
 58J32;
 58Z05;
 58Z05;
 47A07
 EPrint:
 J. Funct. Anal. 268 (2015) 634670