An Extension of Mercer's Theorem via Pontryagin Spaces

被引：0

作者：

Menegatto, V. A. ^{[2
]}

Oliveira, C. P. ^{[1
]}

机构：

[1] ICE UNIFEI, Dept Matemat & Comp, BR-37500903 Itajuba, MG, Brazil

[2] ICMC USP, Dept Matemat, BR-13560970 Sao Carlos, SP, Brazil

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2012年 / 74卷 / 03期

基金：

巴西圣保罗研究基金会;

关键词：

Mercer's theorem; integral operators; positive operators; spectral theorem; Krein spaces; Pontryagin spaces; INTEGRAL-OPERATORS; EQUATIONS;

D O I：

10.1007/s00020-012-2008-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend Mercer's theorem to a composition of the form RS, in which R and S are integral operators acting on a space L-2(X) generated by a locally finite measure space (X, nu). The operator R is compact and positive while S is continuous and having spectral decomposition based on well distributed eigenvalues. The proof is based on a Pontryagin space structure for L-2(X) constructed via the operators R and S themselves.

引用

页码：363 / 375

页数：13

共 16 条

[1]

Ando T., 1979, LINEAR OPERATORS KRE

[2]

[Anonymous], 2002, PURE APPL MATH

[3]

[Anonymous], 1974, ERGEBNISSE MATH IHRE

[4]

Azizov T.Y., 1989, PURE APPL MATH

[5]

AZIZOV TY, 1973, IZV AKAD NAUK SSSR M, V37, P639

[6]

Conway J.B., 2000, RADUATE STUDIES MATH, V21

[7]

Dostanic M.R., 1993, PUBL I MATH-BEOGRAD, V54, P63

[8] Eigenvalues of Integral Operators Defined by Smooth Positive Definite Kernels [J].

Ferreira, J. C. ;

Menegatto, V. A. .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2009, 64 (01) :61-81

[9] On the nuclearity of integral operators [J].

Ferreira, Jose C. ;

Menegatto, Valdir A. ;

Oliveira, Claudemir P. .

POSITIVITY, 2009, 13 (03) :519-541

[10]

Iokhvidov I.S, 1981, DOKL AKAD NAUK UKR A, VA6, P15

← 1 2 →