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

  • 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.
Keywords: Weighted Sobolev-Schrödinger product, Friedrichs extension, resolvent mapping

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.

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Published
2021-08-01
How to Cite
[1]
C.- chi Tung and P. D. Lamberti, “On Rellich’s Lemma, the Poincaré inequality, and Friedrichs extension of an operator on complex spaces”, CUBO, vol. 23, no. 2, pp. 265–285, Aug. 2021.
Section
Articles