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_{j}z) 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_{j}z),
where $f(z)$ is a function
analytical in the unit circle.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k00/k004/k00401h.htm

Last modified: February 13, 2001