On Rellich's Lemma, the Poincaré inequality, and Friedrichs extension of an operator on complex spaces

Abstract

This paper is mainly concerned with: (i) a generalization of the Rellich’s Lemma to a Riemann subdomain of a complex space, (ii) the Poincare inequality, and (iii) Friedrichs extension of a Schrodinger type operator. Applications to the eigenfunction expansion problem associated to the modified Laplacian are also given.