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The representation of entire functions by series in solutions of differential equations

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Abstract

An arbitrary entire function with a growth constraint is represented as the limit of a sequence of partial sums of a series comprised of functions of a fundamental system of particular solutions of a differential equation.

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Literature cited

  1. A. F. Leont'ev, “On the representation of entire functions by some general series,” Matem. Sb.,71(113), No. 1, 3–13 (1966).

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  2. V. A. Tkachenko, “On the decomposition of entire functions of finite order in root functions of a differential operator,” Matem. Sb.,89(131), No. 4, 558–568 (1972).

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Authors and Affiliations

  1. Bashkirsk Branch, Academy of Sciences of the USSR, USSR

    Yu N. Frolov

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  1. Yu N. Frolov
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Translated from Matematicheskie Zametki, Vol. 15, No. 2, pp. 229–234, February, 1974.

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Frolov, Y.N. The representation of entire functions by series in solutions of differential equations. Mathematical Notes of the Academy of Sciences of the USSR 15, 129–132 (1974). https://doi.org/10.1007/BF02102392

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  • DOI: https://doi.org/10.1007/BF02102392

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