References
Doeblin, W. (1940). Sur l'ensemble de puissances d'une loi de probabilité,Studia Math.,9, 71–96.
Feller, W. (1966).An Introduction to Probability Theory and its Applications II, John Wiley, New York.
Gnedenko, B. V. and Kolmogorov, A. N. (1949).Limit Distributions for Sum of Independent Random Variables, Moscow, English translation, Addison-Wesley, Cambridge, Mass., 1954.
Laha, R. G. (1961). On a class of unimodal distributions,Proc. Amer. Math. Soc.,21, 181–184.
Lévy, P. (1937).Théorie de l'Addition des Vatiables Aléatoires, Gauthier-Villars, Paris.
Medgyessy, P. (1967). On a new class of unimodal infinitely divisible distribution functions and related topics,Studia Sci. Math. Hungar. 2, 441–446.
Ramachandran, B. and Radhakrishna Rao, C. (1968). Some results on characterizations of the normal and generalized stable laws,Sankhya,30, 125–140.
Shimizu, R. (1965). Certain class of infinitely divisible characteristic functions,Ann. Inst. Statist. Math.,17, 115–132.
Shimizu, R. (1968). Characteristic functions satisfying a functional equation I,Ann. Inst. Statist. Math.,20, 115–132.
Shimizu, R. (1969). Characteristic functions satisfying a functional equation II,Ann. Inst. Statist. Math.,21, 391–405.
Shimizu R. (1970). Corrections to characteristic functions satisfying a functional equation II,Ann. Inst. Statist. Math.,22, 185–186.
Wintner, A. (1936). On a class of fourier transforms,Amer. J. Math.,58, 45–90.
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Shimizu, R. On the domain of partial attraction of semi-stable distributions. Ann Inst Stat Math 22, 245–255 (1970). https://doi.org/10.1007/BF02506340
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DOI: https://doi.org/10.1007/BF02506340