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On Positive Definiteness of Some Functions

✍ Scribed by Victor P Zastavnyi

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 271 KB
Volume: 73
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.1999.1864

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✦ Synopsis

Let \ be a nonnegative homogeneous function on R n . General structure of the set of numerical pairs ($, *), for which the function (1&\ * (x)) $ + is positive definite on R n is investigated; a criterion for positive definiteness of this function is given in terms of completely monotonic functions; a connection of this problem with the Schoenberg problem on positive definiteness of the function exp(&\ * (x)) is found. We also obtain a general sufficient condition of Polya type for a function f ( (x)) to be positive definite on R n .

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