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On Strong Summability of Jacobi-Fourier-Expansions and Smoothness Properties of Functions

✍ Scribed by Thomas Runst; Winfried Sickel

Publisher: John Wiley and Sons
Year: 1980
Tongue: English
Weight: 390 KB
Volume: 99
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19800990110

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✦ Synopsis

The paper deals with approximation properties of JAcoBI-FOURIER-expansions in dependence of smoothness properties of the treated functions. Such relations are wellknown for trigonometrical series, we refer to LEINDLER [6], [7], OSKOLKOV [9], SCHMEIS-SER and SICKEL [ll].

In the same way as in the paper by SCHMEISSER and SICKEL we give sufficient conditions, such that the sum m z Ilf -S I P ' W I ~p , , t . B l P k = l i s finite.

In the first chapter we develop the theory of BESOV spaces with respect to JACOBI polynomials, in the second chapter we apply these results t.0 problems of strong suminability.

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A Separation Property of Positive Defini

A Separation Property of Positive Definite Functions on Locally Compact Groups and Applications to Fourier Algebras

✍ Eberhard Kaniuth; Anthony T. Lau 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 174 KB

For a closed subgroup H of a locally compact group G consider the property that the continuous positive definite functions on G which are identically one on H separate points in G"H from points in H. We prove a structure theorem for almost connected groups having this separation property for every c