Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation
Sbornik. Mathematics, Tome 200 (2009) no. 3, pp. 455-469
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Conditions under which the reciprocal $1/L(\lambda)$ of an entire function with simple zeros $\lambda_k$
can be represented as a series of partial fractions $c_k/(\lambda-\lambda_k)$, $k=1,2,\dots$, are investigated. The possibility of such a representation is characterized, as is conventional, in terms of a particular ‘asymptotically regular’ behaviour of the function $L(\lambda)$. Applications
to complete systems of exponentials on a line interval and to representative systems of exponentials in a convex domain are considered.
Bibliography: 18 titles.
Keywords:
entire function, series of partial fractions, representative systems of exponentials.
@article{SM_2009_200_3_a7,
author = {V. B. Sherstyukov},
title = {Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation},
journal = {Sbornik. Mathematics},
pages = {455--469},
publisher = {mathdoc},
volume = {200},
number = {3},
year = {2009},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2009_200_3_a7/}
}
TY - JOUR AU - V. B. Sherstyukov TI - Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation JO - Sbornik. Mathematics PY - 2009 SP - 455 EP - 469 VL - 200 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_2009_200_3_a7/ LA - en ID - SM_2009_200_3_a7 ER -
%0 Journal Article %A V. B. Sherstyukov %T Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation %J Sbornik. Mathematics %D 2009 %P 455-469 %V 200 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_2009_200_3_a7/ %G en %F SM_2009_200_3_a7
V. B. Sherstyukov. Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation. Sbornik. Mathematics, Tome 200 (2009) no. 3, pp. 455-469. http://geodesic.mathdoc.fr/item/SM_2009_200_3_a7/