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Addendum to the Paper „On the Measurability of Positive Definite and Conditionally Positive Definite Functions”

✍ Scribed by Zoltán Sasvári

Publisher: John Wiley and Sons
Year: 1987
Tongue: English
Weight: 116 KB
Volume: 131
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19871310128

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✦ Synopsis

Let f be a positive definite function on a locally compact abelian group G. In [3] we showed that measurability of 1 on an open neighbourhood of the zero implies measurability of f on G. As a main tool we used a result about the support of f [3, Th. I]. The aim of this note is to simplify the proof of Theorem 1 in [3] and to extend the results of [3] to arbitrary locally compact groups. Instead of the inequality used in [3] we shall need the following one.

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