## 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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Verfasserangaben: Muhammad Akram, Volker Michel urn:nbn:de:hbz:386-kluedo-14809 Schriften zur Funktionalanalysis und Geomathematik (30) Preprint Englisch 2006 2006 Technische Universität Kaiserslautern 11.02.2007 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 5 Naturwissenschaften und Mathematik / 510 Mathematik 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 Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011