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Classes of complex-valued Borel measures with unique determination from restrictions

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This is a survey of results of functional theoretic character regarding the problem of the description of nontrivial classes of measures on the real line, uniquely determined by their values on the semiaxis. The connection of these results and the method of their derivation with the theory of distribution of values, factorization in the Hardy class H, the theory of divisibility of quasipofynomials, and with questions of growth and decrease of analytic functions is discussed.

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Translated from Zapiski Nauchnykh Semlnarov Leningraclskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 233–253, 1989.

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Ostrovskii, I.V., Ulanovskii, A.M. Classes of complex-valued Borel measures with unique determination from restrictions. J Math Sci 63, 246–257 (1993). https://doi.org/10.1007/BF01099315

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  • Analytic Function
  • Real Line
  • Borel Measure
  • Unique Determination
  • Hardy Class