BEHAVIOR OF COEFFICIENTS OF SERIES OF EXPONENTIALS OF FINITE ORDER NEAR THE BOUNDARY

摘要

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 exponentials, we examine the behavior of coefficients of the series expansion in terms of the growth order near the boundary ∂G. We establish two-sided estimates for the order through characteristics depending only on the indices of the series of exponentials and the support function of the domain (these estimates are strong). As a consequence, we obtain a formula for calculating the growth order through the coefficients.