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On Continuity and Decomposition of Positive Definite Functions

✍ Scribed by Zoltán Sasvári

Publisher
John Wiley and Sons
Year
1989
Tongue
English
Weight
329 KB
Volume
140
Category
Article
ISSN
0025-584X

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✦ Synopsis

Let G be a locally compact commutative group and let g and h be positive definite functions on G, which are not identically zero. We show that continuity of gh implies the existence of a character y of Gd (the discrete version of G) such that yg and y h are continuous. As corollary we get a special case of a result of K. DE LEEW and I. GLICKSBERO concerning almost continuous group representations. In the second part of the paper we prove decomposition theorems for positive definite functions defined on a neighbourhood of the zero.

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