Locally Supported Approximate Identities on the Unit Ball

  • We present a constructive theory for locally supported approximate identities on the unit ball in \(\mathbb{R}^3\). The uniform convergence of the convolutions of the derived kernels with an arbitrary continuous function \(f\) to \(f\), i.e. the defining property of an approximate identity, is proved. Moreover, an explicit representation for a class of such kernels is given. The original publication is available at www.springerlink.com

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Author:Muhammad Akram, Volker Michel
URN (permanent link):urn:nbn:de:hbz:386-kluedo-14809
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (30)
Document Type:Preprint
Language of publication:English
Year of Completion:2006
Year of Publication:2006
Publishing Institute:Technische Universität Kaiserslautern
Tag:approximative Identität; explizite Darstellung; lokal kompakt; lokaler Träger
approximate identity; explicit representation; local support; locally compact
GND-Keyword:Faltung <Mathematik> ; Gleichmäßige Approximation ; Kompakter Träger <Mathematik> ; Kugel; Multivariate Approximation
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):41A30 Approximation by other special function classes
41A35 Approximation by operators (in particular, by integral operators)
41A63 Multidimensional problems (should also be assigned at least one other classification number in this section)
44A35 Convolution
86-08 Computational methods

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