Asymptotic properties of entire functions with given laws of distribution of zeros

V. B. Sherstyukov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex Analysis. Entire Functions and Their Applications, Tome 161 (2019), pp. 104-129.

Résumé

This review was compiled from the author's doctoral dissertation defended at the M. V. Lomonosov Moscow State University in February 2017. The author’s results obtained in the last decade are systematized and summarized. The research relates to the classical direction of the theory of entire functions of one variable devoted to the connection between the asymptotic behavior of an entire function and the distribution of its zeros on the complex plane. The results presented are applied to the theory of complete and representing systems of exponents in spaces of analytic functions.

Détail

Keywords: canonical product, entire function, type, indicator, upper and lower zero density, system of exponents, radius of completeness, representing system
Mots-clés : condensation index, decomposition into simple fractions.

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