Geodesic
Behavior of coefficients of series of exponents of finite order near the boundary
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex Analysis. Mathematical Physics, Tome 162 (2019), pp. 15-24

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Let $G$ be a bounded convex domain with a smooth boundary in which a given system of exponents is not complete. For a class of analytic functions in $G$ that can be represented in $G$ by a series of exponents, we examine the behavior of coefficients of the series expansion in terms of the growth order near the boundary $\partial G$. We establish two-sided estimates for the order through characteristics depending only on the indices of the series of exponents and the supporting function of the domain (these estimates are strong). As a consequence, we obtain a formula for calculating the growth order through the coefficients.
Keywords: series of exponents, domain with smooth boundary, behavior near the boundary, order, $R$-order. 
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     author = {A. M. Gaisin and G. A. Gaisina},
     title = {Behavior of coefficients of series of exponents of finite order near the boundary},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {15--24},
     publisher = {mathdoc},
     volume = {162},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_162_a1/}
}
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A. M. Gaisin; G. A. Gaisina. Behavior of coefficients of series of exponents of finite order near the boundary. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex Analysis. Mathematical Physics, Tome 162 (2019), pp. 15-24. http://geodesic.mathdoc.fr/item/INTO_2019_162_a1/