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Positive definite temperature functions and a correspondence to positive temperature functions
Published online by Cambridge University Press: 14 November 2011
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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