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

Chia-chi Tung; Pier Domenico Lamberti

doi:10.4067/S0719-06462021000200265

DOI:

https://doi.org/10.4067/S0719-06462021000200265

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 Poincaré inequality, and (iii) Friedrichs extension of a Schrödinger type operator. Applications to the eigenfunction expansion problem associated to the modified Laplacian are also given.

Keywords

Weighted Sobolev-Schrödinger product , Friedrichs extension , resolvent mapping

Chia-chi Tung Department of Mathematics and Statistics, Minnesota State University, Mankato Mankato, MN 56001, USA.
Pier Domenico Lamberti Dipartimento di Tecnica e Gestione dei Sistemi Industriali (DTG), University of Padova, Stradella S. Nicola 3-36100 Vicenza, Italy.

Pages: 265–285
Date Published: 2021-08-01
Vol. 23 No. 2 (2021)

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