Variational principles for symmetric bilinear forms

✍ Scribed by Jeffrey Danciger; Stephan Ramon Garcia; Mihai Putinar

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 197 KB
• Volume: 281
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200510641

✦ Synopsis

Abstract

Every compact symmetric bilinear form B on a complex Hilbert space produces, via an antilinear representing operator, a real spectrum consisting of a sequence decreasing to zero. We show that the most natural analog of Courant's minimax principle for B detects only the evenly indexed eigenvalues in this spectrum. We explain this phenomenon, analyze the extremal objects, and apply this general framework to the Friedrichs operator of a planar domain and to Toeplitz operators and their compressions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)