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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
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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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\pages 301--312
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http://mi.mathnet.ru/eng/mz1511https://doi.org/10.4213/mzm1511 http://mi.mathnet.ru/eng/mz/v61/i3/p367
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This publication is cited in the following articles:
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Sedletskii, AM, “Bases occurring in the solution of equations of mixed type”, Differential Equations, 35:4 (1999), 507
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B. N. Khabibullin, “Stability of Completeness for Systems of Exponentials on Compact Convex Sets in $\mathbb C$”, Math. Notes, 72:4 (2002), 542–550
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A. M. Sedletskii, “Analytic Fourier Transforms and Exponential Approximations. I”, Journal of Mathematical Sciences, 129:6 (2005), 4251–4408
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V. P. Zastavnyi, “A Theorem on the Zeros of Entire Functions and Its Application”, Math. Notes, 75:2 (2004), 175–189
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A. M. Sedletskii, “On the Stability of the Uniform Minimality of a Set of Exponentials”, Journal of Mathematical Sciences, 155:1 (2008), 170–182
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V. P. Zastavnyi, “On Zeros of Entire Functions of Special Form”, Math. Notes, 83:1 (2008), 23–30
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Hryniv, RO, “ON ZEROS OF SOME ENTIRE FUNCTIONS”, Transactions of the American Mathematical Society, 361:4 (2009), 2207
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