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The representation of regular functions by Dirichlet series

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Abstract

It is proved that if a system of exponents has the property that any function regular in a closed convex domain ¯G can be represented in an open domain G by a Dirichlet series, then any function regular only in G can be represented in G by a Dirichlet series with the same system of exponents. A study is made of the representation of functions regular in ¯G by Dirichlet series that converge in ¯G.

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Literature cited

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Authors and Affiliations

  1. Mathematics Institute, Academy of Sciences of the Ukrainian SSR, USSR

    Yu. I. Mel'nik

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  1. Yu. I. Mel'nik
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Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 641–651, May, 1977.

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Mel'nik, Y.I. The representation of regular functions by Dirichlet series. Mathematical Notes of the Academy of Sciences of the USSR 21, 360–366 (1977). https://doi.org/10.1007/BF01788232

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  • DOI: https://doi.org/10.1007/BF01788232

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