Schrödinger operators with purely discrete spectrum

Abstract

We prove that $-\Delta +V$ has purely discrete spectrum if $V\geq 0$ and, for all $M$, $|{\{x\mid V(x) < M\}}|<\infty$ and various extensions.

Key words: Compact resolvent, Schrödinger operators.

Full Text

Article Information

Title	Schrödinger operators with purely discrete spectrum
Source	Methods Funct. Anal. Topology, Vol. 15 (2009), no. 1, 61-66
MathSciNet	MR2502639
Milestones	Received 17/10/2008
Copyright	The Author(s) 2009 (CC BY-SA)

Authors Information

Barry Simon
Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, USA 17/10/2008

Citation Example

Barry Simon, Schrödinger operators with purely discrete spectrum, Methods Funct. Anal. Topology 15 (2009), no. 1, 61-66.

BibTex

@article {MFAT495,
    AUTHOR = {Simon, Barry},
     TITLE = {Schrödinger operators with purely discrete spectrum},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {15},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {61-66},
      ISSN = {1029-3531},
  MRNUMBER = {MR2502639},
       URL = {http://mfat.imath.kiev.ua/article/?id=495},
}