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Mat. Zametki, 1997, Volume 61, Issue 3, Pages 367–380 (Mi mz1511)  

This article is cited in 7 scientific papers (total in 7 papers)

Entire functions of Bernstein's class that are not Fourier–Stieltjes transforms

A. M. Sedletskii

M. V. Lomonosov Moscow State University

Abstract: We consider certain subclasses of the class of entire functions of exponential type bounded on the real axis. We construct functions that belong to these subclasses but are not Fourier–Stieltjes transforms. Particular attention is given to the distribution of zeros of such functions. The results obtained allow us to study the stability of completeness of systems of exponentials in $C$ and $L_p$ under small perturbations of the exponents.

DOI: https://doi.org/10.4213/mzm1511

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English version:
Mathematical Notes, 1997, 61:3, 301–312

Bibliographic databases:

UDC: 517.5
Received: 10.07.1995

Citation: A. M. Sedletskii, “Entire functions of Bernstein's class that are not Fourier–Stieltjes transforms”, Mat. Zametki, 61:3 (1997), 367–380; Math. Notes, 61:3 (1997), 301–312

Citation in format AMSBIB
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\paper Entire functions of Bernstein's class that are not Fourier--Stieltjes transforms
\jour Mat. Zametki
\yr 1997
\vol 61
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\pages 367--380
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\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 3
\pages 301--312
\crossref{https://doi.org/10.1007/BF02355412}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sedletskii, AM, “Bases occurring in the solution of equations of mixed type”, Differential Equations, 35:4 (1999), 507  mathnet  mathscinet  zmath  isi
    2. B. N. Khabibullin, “Stability of Completeness for Systems of Exponentials on Compact Convex Sets in $\mathbb C$”, Math. Notes, 72:4 (2002), 542–550  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. M. Sedletskii, “Analytic Fourier Transforms and Exponential Approximations. I”, Journal of Mathematical Sciences, 129:6 (2005), 4251–4408  mathnet  crossref  mathscinet  zmath
    4. V. P. Zastavnyi, “A Theorem on the Zeros of Entire Functions and Its Application”, Math. Notes, 75:2 (2004), 175–189  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. A. M. Sedletskii, “On the Stability of the Uniform Minimality of a Set of Exponentials”, Journal of Mathematical Sciences, 155:1 (2008), 170–182  mathnet  crossref  mathscinet  zmath  elib
    6. V. P. Zastavnyi, “On Zeros of Entire Functions of Special Form”, Math. Notes, 83:1 (2008), 23–30  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. Hryniv, RO, “ON ZEROS OF SOME ENTIRE FUNCTIONS”, Transactions of the American Mathematical Society, 361:4 (2009), 2207  crossref  mathscinet  zmath  isi  scopus  scopus
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