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


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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How to Cite
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.