An approximation theorem for entire functions of exponential type and stability of zero sequences

Journal Article · Sat Feb 28 04:00:00 EST 2004 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2004V195N01ABEH000797; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21260460

Khabibullin, B N ^[1]

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1. Bashkir State University, Ufa (Russian Federation)

Let L be an entire function of exponential type in C with indicator function h{sub L}; let {lambda}={l_brace}{lambda}{sub n}{r_brace}, n=1,2,..., be a subsequence of zeros of the entire function of exponential type L{ne}0; let {gamma}={l_brace}{gamma}{sub n}{r_brace} be a complex number sequence and assume that {sigma}{sub n}|1/{lambda}{sub n} - 1/{gamma}{sub n}|<{infinity}. A simple construction of a sequence of entire functions of exponential type {l_brace}L{sub n}{r_brace} transforming {lambda} into a subsequence {gamma} of zeros of an entire function of exponential type G{ne}0 such that h{sub G}=h{sub L} 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.

• OSTI ID: 21260460
• Journal Information: Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 1 Vol. 195; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

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ANALYTIC FUNCTIONS
APPROXIMATIONS
COMPLEX MANIFOLDS
MATHEMATICAL SPACE
STABILITY