An extension of Mercer's theory to \(L^p\)
type: Item
instance of: scholarly article
title: An extension of Mercer's theory to \(L^p\)
zbMATH Open document ID: 1261.45001
published in: Positivity
publication date: 2013-01-03T00:00:00Z
review text: The paper consist of four sections. In Section 1, the author considers an integral operator generated by a Mercer like kernel \(K\). In Section 2, Mercer's theory is extended to the convergence in the \(p\)-mean under suitable assumptions. Further, a series representations on the convergence in the \(p\)-mean of functions, in the range of a generalized power of the operator, and a recovery formula is obtained. The spectral properties of a modified version of an integral operator acting on \(L^p(X,v)\) in Section 4 is used to estimate the approximation numbers.
reviewed by: Deshna Loonker
Mathematics Subject Classification ID: 45C05
Mathematics Subject Classification ID: 45P05
zbMATH DE Number: 6121583
zbMATH Keywords: positive integral operator
zbMATH Keywords: eigenvalues
zbMATH Keywords: positive definite kernels
zbMATH Keywords: Mercer's theory
zbMATH Keywords: norm estimates
zbMATH Keywords: Mercer like kernel
author: José C. Ferreira
author: Valdir A. Menegatto
MaRDI profile type: Publication
full work available at URL: s11117-011-0118-8
OpenAlex ID: W2005104573
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DOI: 10.1007/S11117-011-0118-8
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description: scientific article; zbMATH DE number 6121583