Abstract:
Let L
be an entire function of exponential type
in C with indicator function hL;
let
Λ={λn}, n=1,2,…,
be a subsequence of
zeros of the entire function of exponential type
L≢0;
let Γ={γn}
be a complex number sequence and assume that
∑n|1λn−1γn|<∞.
A simple construction of a sequence of entire functions of
exponential type {Ln} transforming Λ
into a subsequence Γ
of zeros of an entire function of exponential type
G≢0
such that hG=hL
is put forward
(an approximation theorem). This result is applied to stability
problems of zero sequences and non-uniqueness sequences
for spaces of entire functions of exponential type
with constraints on the indicators and to the
problem of the stability of the completeness property of
exponential systems in the space of germs of analytic
functions on a compact convex set.
Citation:
B. N. Khabibullin, “An approximation theorem for entire functions of
exponential type and stability of zero sequences”, Sb. Math., 195:1 (2004), 135–148
\Bibitem{Kha04}
\by B.~N.~Khabibullin
\paper An approximation theorem for entire functions of
exponential type and stability of zero sequences
\jour Sb. Math.
\yr 2004
\vol 195
\issue 1
\pages 135--148
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Linking options:
https://www.mathnet.ru/eng/sm797
https://doi.org/10.1070/SM2004v195n01ABEH000797
https://www.mathnet.ru/eng/sm/v195/i1/p143
This publication is cited in the following 2 articles:
E. G. Kudasheva, B. N. Khabibullin, “Variation of subharmonic function under transformation of its Riesz measure”, Zhurn. matem. fiz., anal., geom., 3:1 (2007), 61–94
B. N. Khabibullin, “Spectral synthesis for the intersection of invariant subspaces of holomorphic functions”, Sb. Math., 196:3 (2005), 423–445