The order of growth of an exponential series near the boundary of the convergence domain
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G. A. Gaisina
Translated by: V. V. Kapustin - St. Petersburg Math. J. 33 (2022), 449-463
- DOI: https://doi.org/10.1090/spmj/1708
- Published electronically: May 5, 2022
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Abstract:
For a class of analytic functions in a bounded convex domain $G$ that admit an exponential series expansion in $D$, the behavior of the coefficients of this expansion is studied in terms of the growth order near the boundary $\partial G$. In the case where $G$ has a smooth boundary, unimprovable two-sided estimates are established for the order via characteristics depending only on the exponents of the exponential series and the support function of $G$. As a consequence, a formula is obtained for the growth of the exponential series via the coefficients and the support function of the convergence domain $G$.References
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Bibliographic Information
- G. A. Gaisina
- Affiliation: Bashkir State University, Z. Validi str. 32, 450076 Ufa, Russia
- Email: gaisinaga@mail.ru
- Received by editor(s): January 13, 2020
- Published electronically: May 5, 2022
- Additional Notes: The research was done in the framework of the development program of the Scientific-educational mathematical center of the Privolzhski Federeal Region, additional agreement no. 075-02-2020-1421/1 to agreement no. 075-02-2020-1421
- © Copyright 2022 American Mathematical Society
- Journal: St. Petersburg Math. J. 33 (2022), 449-463
- MSC (2020): Primary 30D10
- DOI: https://doi.org/10.1090/spmj/1708
- MathSciNet review: 4445778