Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T23:29:12.494Z Has data issue: false hasContentIssue false

Positive definite functionals in Banach spaces

Published online by Cambridge University Press:  09 April 2009

G. G. Hamedani
Affiliation:
Arya-Mehr University of Technology, Tehran, Iran. Michigan State University, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We establish a version of Bochner Theorem due to S. Boylan for Banch spaces with a basis.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1977

References

Boylan, S. L. (1975), ‘Positive definite functionals, function-space transforms and abstract Wiener spaces’, Duke Math. J., 42, 549557.CrossRefGoogle Scholar
Day, M. M. (1962), Normed linear spaces, 2ndrev. ed. (Academic Press, New York: Springer-Verlag, Berlin). MR26#2847.Google Scholar
Gross, L. (1963), ‘Harmonic analysis on Hilbert space’. Mem. Amer. Math. Soc 46. MR28≠4304.Google Scholar
Hamedani, G. G. and Mandrekar, V. (1973), ‘Inversion formulae for the probability measures on Banach spaces’, Trans. Amer. Math. Soc., 180, 143169.Google Scholar
Kuelbs, J. (1970), ‘Gaussian measures on a Banach space’. J. Functional Analysis 5, 354367. MR41≠4639.Google Scholar
Kuelbs, J. and Mandrekar, V. (1972), ‘Harmonic anlaysis on F-spaces with a basis’, Trans. Amer. Math. Soc. 169, 113152.Google Scholar
Sazanov, V. (1958), ‘Remarks on characteristic functionals’. Teor. Verojatnost. i Primenen. 3, 201205Google Scholar
Theor. Probability Appl. 3 (1958). 188192. MR20#4882.CrossRefGoogle Scholar