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2006 Positive definite matrices and integral equations on unbounded domains
Jorge Buescu, A. C. Paixão
Differential Integral Equations 19(2): 189-210 (2006).


The kernel of a continuous positive integral operator on an interval $I$ is a Moore matrix on $I$. We show that, under minimal differentiability assumptions, this implies that the kernel satisfies a 2-parameter family of differential inequalities. These inequalities ensure that, for unbounded $I$, the corresponding integral operator is exceptionally well behaved: it is compact and thus the eigenfunctions for its discrete spectrum have the differentiability of the kernel and satisfy sharp Sobolev bounds, the symmetric mixed partial derivatives are again kernels of positive operators and the differentiated eigenfunction series converge uniformly and absolutely. Converse results are derived.


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Jorge Buescu. A. C. Paixão. "Positive definite matrices and integral equations on unbounded domains." Differential Integral Equations 19 (2) 189 - 210, 2006.


Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.45019
MathSciNet: MR2194503

Primary: 46E22
Secondary: ‎45P05‎ , 47G10

Rights: Copyright © 2006 Khayyam Publishing, Inc.


Vol.19 • No. 2 • 2006
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