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The domain of regularity of the limit function of a sequence of analytic functions

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Abstract

Letf (z) be an entire function λn(n=0,1,2,...) complex numbers, such that the system f(λn ∞n=0 is not complete in the circle ¦z¦<R and let the sequence Qn(z) have the form\(\sum\nolimits_{k = 0}^{p_n } {\alpha _{nk} } f(\lambda _k \cdot z)\). We study the properties of the limit function of the sequence Qn(z) in the case when

$$f(z) = 1 + \sum\nolimits_{n = 1}^\infty {\frac{{z^n }}{{P(1)P(2)...P(n)}}} ,$$

. where P(z) is a polynomial having at least one negative integral root.

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Authors and Affiliations

  1. Physics and Mathematics Section of the Bashkir Division of the Academy of Sciences of the USSR, USSR

    V. V. Napalkov

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  1. V. V. Napalkov
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Translated from Matematicheskie Zametki, Vol. 12, No. 6, pp. 681–692, December, 1972.

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Napalkov, V.V. The domain of regularity of the limit function of a sequence of analytic functions. Mathematical Notes of the Academy of Sciences of the USSR 12, 849–855 (1972). https://doi.org/10.1007/BF01156043

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  • DOI: https://doi.org/10.1007/BF01156043

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