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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Metadaten
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
Date of the Publication (Server):2007/02/11
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:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification (mathematics):41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A30 Approximation by other special function classes
41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A35 Approximation by operators (in particular, by integral operators)
41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A63 Multidimensional problems (should also be assigned at least one other classification number in this section)
44-XX INTEGRAL TRANSFORMS, OPERATIONAL CALCULUS (For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10) / 44Axx Integral transforms, operational calculus / 44A35 Convolution
86-XX GEOPHYSICS [See also 76U05, 76V05] / 86-08 Computational methods
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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