## 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

Author: Muhammad Akram, Volker Michel urn:nbn:de:hbz:386-kluedo-14809 Schriften zur Funktionalanalysis und Geomathematik (30) Preprint English 2006 2006 Technische Universität Kaiserslautern approximative Identität; explizite Darstellung; lokal kompakt; lokaler Trägerapproximate identity; explicit representation; local support; locally compact Faltung ; Gleichmäßige Approximation ; Kompakter Träger ; Kugel; Multivariate Approximation Fachbereich Mathematik 510 Mathematik 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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