FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2000, VOLUME 6, NUMBER 4, PAGES 955-976
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 $\sum\limits_{j=1}^{\infty}
d_{j} f(\lambda_{j})$ ,
where $f(\lambda)$ is
an analytical in the circle
$|\lambda| < 1$
vector-valued function, the values of which are vectors
from $H$ ,
$|\lambda_{j}| \nearrow 1$ .
The proved theorems
generalize the well-known results about expansion
of analytical functions in a rational series of the form
$\sum\limits_{j=1}^{\infty}
\frac{d_{j}}{1-\lambda_{j}z}$ and also the results
of the author about expansion of analytical functions
in a series of the form
$\sum\limits_{j=1}^{\infty}
d_{j} f(\lambda_{j}z)$ ,
where $f(z)$
is a function analytical in the unit circle.
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Last modified: February 13, 2001