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On the Positive Definiteness of a Functional

Published online by Cambridge University Press:  20 November 2018

J. N. Pandey
J. N. Pandey*
Affiliation:
Centre de Recherches Mathématiques, Université de Montréal Montréal, Que. H3C 3J7
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Abstract

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In this note, we have shown that the set of conditions given by Gel'fand and Vilenkin for the positive definiteness of a functional L(ϕ) [1, Theorem 7, p. 285] though sufficient is not necessary, thereby providing an answer to an open problem posed by them [1, Theorem 7, p. 285].

Keywords

46F1046E4060J30Positive definite functionalpositive definite functionGeneralized Stochastic ProcessStochastic processes with independent values at every point
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 2 , 01 June 1979 , pp. 203 - 206
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Gel'fand, I. M. and Vilenkin, N. Ya, Generalized functions, Volume 4, 1964 Academic Press.Google Scholar
2. Hirschman, I. I. and Widder, D. V., The convolution transform, 1955, Princeton University Press.Google Scholar
3. Karlin, Samuel, Total positivity, Volume I, 1968, Stanford University Press.Google Scholar