FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 4, PAGES 955-976

Analogues of the rational series in the locally convex space

E. N. Alexeeva

Abstract

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The aim of the paper is to study the conditions of expansion of vectors of a complete locally convex space $H$ in a series of the form $$å_j=1^¥ d_j f(l_j), where $f($l) is an analytical in the circle $|$l| < 1 vector-valued function, the values of which are vectors from $H$, $\$\; |$l_j| \nearrow 1 $. The proved theorems generalize the well-known results about expansion of analytical functions in a rational series of the form $$å_j=1^¥ (d_j)/(1-l_jz) and also the results of the author about expansion of analytical functions in a series of the form $$å_j=1^¥ d_j f(l_jz), where $f(z)$ is a function analytical in the unit circle.

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Last modified: February 13, 2001