FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 3, PAGES 637-652

On the system $\{f($l_jz)} series

E. N. Alexeeva

Abstract

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The aim of the paper is to search the conditions of the expansion of the functions analytical in a unit circle in a series of the $$å_j=1^¥d_jf(l_jz) kind, where $f(z)$ is the function analytical in a unit circle, $|$l_j| < 1. The proved theorems contain as a special case the well-known results about the expansion of analytical functions in the rational series of the form $$å_j=1^¥(d_j)/(1-l_jz).

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Last modified: January 20, 2000