Harmonic analysis on $F$-spaces with a basis
HTML articles powered by AMS MathViewer
- by J. Kuelbs and V. Mandrekar PDF
- Trans. Amer. Math. Soc. 169 (1972), 113-152 Request permission
Abstract:
We establish Bochner’s theorem and the Levy continuity theorem in the case that the underlying space is a real $F$-space with a basis, and then examine the infinitely divisible probability measures on a class of such spaces.References
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- Leonard Gross, Harmonic analysis on Hilbert space, Mem. Amer. Math. Soc. 46 (1963), ii+62. MR 161095
- J. Kuelbs and V. Mandrekar, Harmonic analysis on certain vector spaces, Trans. Amer. Math. Soc. 149 (1970), 213–231. MR 301162, DOI 10.1090/S0002-9947-1970-0301162-2
- John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
- Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Teor. Veroyatnost. i Primenen. 1 (1956), 177–238 (Russian, with English summary). MR 0084896
- Ju. V. Prohorov and V. V. Sazonov, Some results related to Bochner’s theorem, Teor. Verojatnost. i Primenen. 6 (1961), 87–93 (Russian, with English summary). MR 0149239
- V. Sazonov, On characteristic functionals, Teor. Veroyatnost. i Primenen. 3 (1958), 201–205 (Russian, with English summary). MR 0098423
- Nicolas Vakhania, Sur une propriété des répartitions normales de probabilités dans les espaces $l_{p}\,(1\leq p<\infty )$ et $H$, C. R. Acad. Sci. Paris 260 (1965), 1334–1336 (French). MR 174075
- Nicolas Vakhania, Sur les répartitions de probabilités dans les espaces de suites numériques, C. R. Acad. Sci. Paris 260 (1965), 1560–1562 (French). MR 174076
- Adriaan Cornelis Zaanen, Linear analysis. Measure and integral, Banach and Hilbert space, linear integral equations, Interscience Publishers Inc., New York; North-Holland Publishing Co., Amsterdam; P. Noordhoff N. V., Groningen, 1953. MR 0061752
- S. R. S. Varadhan, Limit theorems for sums of independent random variables with values in a Hilbert space, Sankhyā Ser. A 24 (1962), 213–238. MR 171305
- Alejandro D. de Acosta, Existence and convergence of probability measures in Banach spaces, Trans. Amer. Math. Soc. 152 (1970), 273–298. MR 267614, DOI 10.1090/S0002-9947-1970-0267614-9
- L. Le Cam, Remarques sur le théorème limite central dans les espaces localement convexes, Les probabilités sur les structures algébriques (Actes Colloq. Internat. CNRS, No. 186, Clermont-Ferrand, 1969) Éditions Centre Nat. Recherche Sci., Paris, 1970, pp. 233–249 (French, with English summary). Avec commentaire en anglais par R. M. Dudley. MR 0410832
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 169 (1972), 113-152
- MSC: Primary 60B05; Secondary 28A40
- DOI: https://doi.org/10.1090/S0002-9947-1972-0341544-8
- MathSciNet review: 0341544