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On the decomposition of the convolution of a Gaussian and Poisson distribution on locally compact Abelian groups. (English) Zbl 0518.60012

MSC:

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
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[1] Bourbaki, N., (General Topology (1966), Herman: Herman Paris), [English transl., Addison-Wesley, Reading, Mass.] · Zbl 0145.19302
[2] Cuppens, R., Sur la décomposition de la composition d’une loi normale et d’une loi de Poisson, C. R. Acad. Sci., 262, 1113-1116 (1966) · Zbl 0139.35504
[3] Feldman, G. M., On the decomposition of Gaussian distributions on groups, Theory Probab. Appl., 22, 133-140 (1977) · Zbl 0378.60006
[4] Feldman, G. M., Gaussian distributions on locally compact Abelian groups, Theory Probab. Appl., 23, 529-542 (1978) · Zbl 0421.60009
[5] Levin, B. Ya, (Distribution of Zeros of Entire Functions (1956), Gostekhizdat: Gostekhizdat Moscow). (Distribution of Zeros of Entire Functions (1956), Gostekhizdat: Gostekhizdat Moscow), AMS translations of mathematical monographs, Vol. 5 (1964), English transl.
[6] Linnik, Yu. V., On the decomposition of the convolution of Gaussian and Poissonian laws, Theory Probab. Appl., 2, 31-57 (1957)
[7] AMS translations of mathematical monographs (1977), No. 48 · Zbl 0358.60020
[8] Markushevič, A. I., (The Theory of Analytic Functions, Vol. 2 (1968), Nauka: Nauka Moscow), [English transl., 2nd ed., chelsea, new York, 1997.]
[9] Ostrovskii, I. V., The multidimensional analog of Yu. V. Linnik’s theorem of decompositions of a convolution of Gaussian and Poisson laws, Theory Probab. Appl., 10, 673-677 (1965) · Zbl 0171.39505
[10] Parthasarathy, K. R.; Ranga Rao, R.; Varadhan, S. R.S, Probability distributions on locally compact Abelian groups, Illinois J. Math., 7, 337-369 (1963) · Zbl 0129.10902
[11] Rukhin, A. L., Some statistical and probabilitic problems on groups, (Proc. Steklov Inst. Math. (1970)), 111, [English transl., AMS, Providence, R.I., 1972]
[12] Sazonov, V. V.; Tutubalin, V. N., Probability distributions on topological groups, Theory Probab. Appl., 11, 1-45 (1966) · Zbl 0171.38701
[13] Weil, A., Integration on topological groups and its application, (Actualités Sci. Indust., 869 (1942), Herman: Herman Paris), [English transl., Edwards Brothers, Inc., 1942]
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