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 Mat. Zametki, 1977, Volume 21, Issue 5, Pages 627–639 (Mi mz7995)

Series of rational fractions with rapidly decreasing coefficients

T. A. Leont'eva

M. V. Lomonosov Moscow State University

Abstract: In [1] it was shown that if a function $f(z)$, analytic inside the unit disk, is representable by a series $\sum_{n=1}^\infty\frac{\mathscr A_n}{1-\lambda_nz}$ and if the coefficients $\mathscr A_n$ rapidly tend to zero, then $f(z)$ satisfies some functional equation $M_L(f)=0$. In the present paper the converse problem is solved. It is shown that if $f(z)$ satisfies the equation $M_L(f)=0$, then the expansion coefficients rapidly tend to zero.

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English version:
Mathematical Notes, 1977, 21:5, 353–360

Bibliographic databases:

UDC: 517.5

Citation: T. A. Leont'eva, “Series of rational fractions with rapidly decreasing coefficients”, Mat. Zametki, 21:5 (1977), 627–639; Math. Notes, 21:5 (1977), 353–360

Citation in format AMSBIB
\Bibitem{Leo77} \by T.~A.~Leont'eva \paper Series of rational fractions with rapidly decreasing coefficients \jour Mat. Zametki \yr 1977 \vol 21 \issue 5 \pages 627--639 \mathnet{http://mi.mathnet.ru/mz7995} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=460605} \zmath{https://zbmath.org/?q=an:0399.30004|0362.30002} \transl \jour Math. Notes \yr 1977 \vol 21 \issue 5 \pages 353--360 \crossref{https://doi.org/10.1007/BF01788231} 

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This publication is cited in the following articles:
1. V. B. Sherstyukov, “Dual characterization of absolutely representing systems in inductive limits of Banach spaces”, Siberian Math. J., 51:4 (2010), 745–754
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