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Positive definite temperature functions and a correspondence to positive temperature functions

Published online by Cambridge University Press:  14 November 2011

Soon-Yeong Chung
Soon-Yeong Chung
Affiliation:
Department of Mathematics, Sogang University, Seoul 121-742, Korea
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Synopsis

Positive definite temperature functions u(x, t) in ℝn+1 = {(x, t)| x ∈ ℝn,t > 0} are characterised by

where μ is a positive measure satisfying that for every ℰ > 0,

is finite. A transform is introduced to give an isomorphism between the class ofall positive definite temperature functions and the class of all possible temperature functions in Then correspondence given by generalises the Bochner–Schwartz Theorem for the Schwartz distributions and extends Widder's correspondence characterising some subclass of the positive temperature functions by the Fourier-Stieltjes transform.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 5 , 1997 , pp. 947 - 961
Copyright
Copyright © Royal Society of Edinburgh 1997

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