Variational principles for symmetric bilinear forms

被引：8

作者：

Danciger, Jeffrey ^{[2
]}

Garcia, Stephan Ramon ^{[1
]}

Putinar, Mihai ^{[3
]}

机构：

[1] Pomona Coll, Dept Math, Claremont, CA 91711 USA

[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[3] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

来源：

MATHEMATISCHE NACHRICHTEN | 2008年 / 281卷 / 06期

关键词：

symmetric bilinear form; Friedrichs operator; singular values; compact operator; compressed Toeplitz operator; Courant principle; minimax theorem;

D O I：

10.1002/mana.200510641

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

引用

页码：786 / 802

页数：17

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