Abstract:
Conditions under which the reciprocal 1/L(λ) of an entire function with simple zeros λk
can be represented as a series of partial fractions ck/(λ−λk), k=1,2,…, 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(λ). 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.
Citation:
V. B. Sherstyukov, “Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation”, Sb. Math., 200:3 (2009), 455–469
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\paper Representation of the reciprocal of an entire function by series of partial fractions and exponential approximation
\jour Sb. Math.
\yr 2009
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\pages 455--469
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Linking options:
https://www.mathnet.ru/eng/sm4034
https://doi.org/10.1070/SM2009v200n03ABEH004004
https://www.mathnet.ru/eng/sm/v200/i3/p147
This publication is cited in the following 3 articles:
V. B. Sherstyukov, “Asymptotic properties of entire functions with given laws of distribution of zeros”, J. Math. Sci. (N. Y.), 257:2 (2021), 246–272
Ufa Math. J., 8:2 (2016), 104–111
V. B. Sherstyukov, “Expanding the reciprocal of an entire function with zeros in a strip in a Kreǐn series”, Sb. Math., 202:12 (2011), 1853–1871
Citation in format AMSBIB
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