Positive definite matrices and differentiable reproducing kernel inequalities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:320

Article

Buescu, Jorge ; Paixao, A. C.

关键词: positive definite matrices;    reproducing kernels;    inequalities;   

DOI  :  10.1016/j.jmaa.2005.06.088

来源: Elsevier

【 摘 要 】

Let I subset of R be a interval and k: I-2 -> C be a reproducing kernel on I. By the Moore-Aronszajn theorem, every finite matrix k(x(i), x(j)) is positive semidefinite. We show that, as a direct algebraic consequence, if k(x, y) is appropriately differentiable it satisfies a 2-parameter family of differential inequalities of which the classical diagonal dominance is the order 0 case. An application of these inequalities to kernels of positive integral operators yields optimal Sobolev norm bounds. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

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