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A relationship between the maximum modulus and Taylor coefficients of entire functions of several complex variables

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Abstract

We present results on the relationship between the growth of the maximum modulus and the decay of Taylor coefficients of entire functions of several variables. The results are obtained by two different methods, the first of which had been proposed earlier by Oskolkov for the one-dimensional case, and the second is based on the use of the Legendre-Jung-Fenchel conjugates of the weight functions. Attention is mainly paid to the characterization of the growth of entire functions with respect to the conjunction of variables; however, some results are obtained for the case in which there is different growth with respect to different variables.

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Authors and Affiliations

  1. Rostov State University, Rostov, USSR

    Yu. F. Korobeinik

Authors
  1. Yu. F. Korobeinik
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Translated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 238–258, August, 1997.

Translated by N. K. Kulman

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Korobeinik, Y.F. A relationship between the maximum modulus and Taylor coefficients of entire functions of several complex variables. Math Notes 62, 198–215 (1997). https://doi.org/10.1007/BF02355908

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  • DOI: https://doi.org/10.1007/BF02355908

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