Abstract
The topological description of the class of characteristic functionals of probability measures in infinite dimensional spaces means the description of this class in terms of the positive definiteness and continuity in an appropriately chosen topology. The almost final results obtained in this direction are presented in [9] and [16] (especially see Ch.IV and VI). Here we give slight refinements of known results and discuss some unsolved problems which are related to questions considered and are also of independent interest.
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References
Gross L. (1963). Harmonic analysis on Hilbert space. Mem. Amer. Math. Soc. 46, 1–62.
Kalton, N. J. (1985). Banach spaces embedding into L 0. Israel J. Math. 54, 305–319.
Kuelbs, J. (1973). Fourier analysis on linear metric spaces. Trans. Amer. Math. Soc. 181, 293–311.
Madrecki, A. (1985). On Sazonov type topology in p-adic Banach spaces. Math. Z. 188, 225–236.
Mathe, P. (1990). s-numbers in information-based complexity. J. Complexity 6, 41–66.
Maurey, B. (1974). Theoremes de factorization pur les Operateurs lineaires a valeurs dans les espaces L p. Asterisque 11, 1–163.
Maurey, B. and G. Pisier (1976). Series de variables aleatoires vectorieles independantes et proprietes geometriques des espaces de Banach. Studia Math. 58, 3 49–90.
Mushtari, D. (1973). Some piroblems of the theory of probability measures in linear spaces. Teor. Veroyat. Prim. 18, 66–77.
Mushtari, D. (1989). Probabilities and topologies in Banach spaces. Kazan University Publishers, Kazan.
Okazaki, Y. (1979). L 0-embedding of a linear metric space. Mem. Fac. Sci. Kyushu Univ. Ser. A 33, 391–398.
Okazaki, Y. (1980). Harmonic analysis in a Banach space. Mem. Fac. Sci. Kyoshu Univ. Ser. A. 34, 27–69.
Sazonov, V. V. (1958). A remark on characteristic functionals. Teor. Veroyat Prim. 3, 201–205.
Tarieladze, V. I. (1987). On the uniqueness theorem for Fourier transform. Proc. Muskhelishvili Inst. Comp. Math. Acad. Sci. Georgian SSR 28, 195–207.
Tarieladze, V. I. (1988). On the Fourier topology of infinite dimensional spaces. Proc. Muskhelishvili Inst. Comp. Math. Acad. Sei. Georgian SSR 28, 179–191.
Tarieladze, V. I. (1989). The topological description of characteristic functionals in certain groups. Tear. Veroyat. Prim. 34, 95–106.
Vakhania, N. N., V. I. Tarieladze, and S. A. Chobanyan (1987). Probability Distributions on Banach Spaces. D. Reidel, Dordrecht.
Vershik, A. M. and V. N. Sudakov (1969). Probability measures in infinite dimensional spaces. Zapiski Nauch. Sem. LOMI 12, 7–67.
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Tarieladze, V.I. (1994). On the Topological Description of Characteristic Functionals in Infinite Dimensional Spaces. In: Hoffmann-Jørgensen, J., Kuelbs, J., Marcus, M.B. (eds) Probability in Banach Spaces, 9. Progress in Probability, vol 35. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0253-0_14
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DOI: https://doi.org/10.1007/978-1-4612-0253-0_14
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