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Measures on locally compact abelian groups, whose n-fold convolutions are determined by the restrictions to a massive set

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Abstract

The paper deals with an area that studies measures that are uniquely determined by their restriction to a sufficiently abundant set. This area began to develop in the 1970s under the initiative of V. M. Zolotarev. Its present state is reflected in [1, 2], where a detailed bibliography can be found.

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References

  1. H.-J. Rossberg, B. Jesiak, and G. Siegel, Analytic Methods of Probability Theory, Akademie-Verlag, Berlin (1985).

    Google Scholar 

  2. I. V. Ostrovskii and A. M. Ulanovskii, "Classes of complex-valued Borel measures with unique determination by restrictions," Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,170, 233–253 (1989).

    Google Scholar 

  3. I. A. Ibragimov, "On the determination of an infinitely divisible distribution function from its values on a semiline," Teor. Veroyatn. Primenen.,22, No. 2, 393–399 (1977).

    Google Scholar 

  4. I. V. Ostrovskii, "Generalization of the Titchmarsh convolution theorem and the complex-valued measures uniquely determined by their restrictions to a half-line," Lecture Notes in Math., No. 1155, Springer, Berlin (1985), pp. 256–283.

    Google Scholar 

  5. A. M. Ulanovskii, "On the unique determination of convolutions of measures inR m, m ≥ 2, by restrictions to sets," Teor. Funkts. Funktsional. Anal. Prilozhen. (Khar'kov), No. 50, 86–90 (1988).

    Google Scholar 

  6. A. I. Il'inskii, "Some remarks on the uniqueness of the extension of measures from subsets to the group Z2 ×R," in: Stability Problems for Stochastic Models (Proc. Internat. Seminar held in Sukhumi, October 1987), Vses. Nauch.-Issled. Inst. Sistem. Issled., Moscow (1988), pp. 55–59.

    Google Scholar 

  7. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. 1, Springer, Berlin (1963).

    Google Scholar 

  8. O. B. Skaskiv, "A generalization of the little Picard theorem," Teor. Funkts. Funktsional. Anal. Prilozhen. (Khar'kov), No. 46, 90–100 (1986).

    Google Scholar 

  9. A. M. Ulanovskii, "Determination of the n-fold convolution of a distribution function from its values on a system of intervals," Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 3, 32–35 (1988).

    Google Scholar 

  10. Yu. V. Linnik (Ju. V. Linnik) and I. V. Ostrovskii, Decomposition of Random Variables and Vectors, Amer. Math. Soc., Providence (1977).

  11. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. 2, Springer, Berlin (1970).

    Google Scholar 

  12. A. A. Gol'dberg, "Some questions of value distribution theory." Appendix to the Russian translation of H. Wittich, Neuere Untersuchungen über eindeutige analytische Funktionen, Fizmatgiz, Moscow (1960), pp. 263–300.

    Google Scholar 

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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 264–270, 1990.

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Ulanovskii, A.M. Measures on locally compact abelian groups, whose n-fold convolutions are determined by the restrictions to a massive set. J Math Sci 68, 588–591 (1994). https://doi.org/10.1007/BF01254286

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