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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Entire functions of sine type and their applications

Authors: R. A. Bashmakov, A. A. Putintseva and P. C. Yulmukhametov
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 22 (2010), nomer 5.
Journal: St. Petersburg Math. J. 22 (2011), 737-750
MSC (2010): Primary 30D15
Published electronically: June 27, 2011
MathSciNet review: 2828826
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Abstract | References | Similar Articles | Additional Information

Abstract: For subharmonic functions that depend only on the real part of $ z$, new constructions of ``sine type functions'' are presented. This term is reserved for entire functions whose deviation from a given function is majorized, everywhere except some collection of disks, by a certain constant. It is shown that the system of exponentials constructed by the zeros of a sine type function for some convex function is complete and minimal in a certain weighted Hilbert space on an interval of the real line.

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  • 1. B. Ja. Levin and Ju. I. Ljubarskiĭ, Interpolation by entire functions belonging to special classes and related expansions in series of exponentials, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), no. 3, 657–702, 704 (Russian). MR 0454019
  • 2. V. S. Azarin, The rays of completely regular growth of an entire function, Mat. Sb. (N.S.) 79 (121) (1969), 463–476 (Russian). MR 0257357
  • 3. R. S. Yulmukhametov, Approximation of subharmonic functions, Anal. Math. 11 (1985), no. 3, 257-282. (Russian) MR 0822590 (88a:31002)
  • 4. Yu. I. Lyubarskiĭ and M. L. Sodin, Analogues of functions of sinusoidal type for convex domains, Preprint no. 17, Fiz.-Tekhn. Inst. Nizkikh Temperatur Akad. Nauk Ukr. SSR, Khar'kov, 1986. (Russian)
  • 5. A. F. Leont'ev, Entire functions. Series of exponentials, Nauka, Moscow, 1983. (Russian) MR 0753827 (86j:30005)
  • 6. V. I. Lutsenko and R. S. Yulmukhametov, Generalization of the Paley-Wiener theorem on weighted spaces, Mat. Zametki 48 (1990), no. 5, 80–87, 159 (Russian); English transl., Math. Notes 48 (1990), no. 5-6, 1131–1136 (1991). MR 1092157,
  • 7. Igor Chyzhykov, Approximation of subharmonic functions of slow growth, Mat. Fiz. Anal. Geom. 9 (2002), no. 3, 509–520. MR 1949807
  • 8. K. P. Isaev, A. A. Putintseva, and R. S. Yulmukhametov, Representation by series in weighted spaces on the real axis, Ufim. Mat. Zh. 1 (2009), no. 1, 16-37. (Russian)
  • 9. B. Ya. Levin, On bases of exponential functions in $ L^2(-\pi,\pi)$, Zap. Fiz.-Mat. Fak. Khar'kov. Gos. Univ. i Khar'kov. Mat. Obshch. 27 (1961), no. 4, 39-48. (Russian)
  • 10. Yurii Lyubarskii and Eugenia Malinnikova, On approximation of subharmonic functions, J. Anal. Math. 83 (2001), 121–149. MR 1828489,

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Additional Information

R. A. Bashmakov
Affiliation: Bashkir State University, Ul. Zaki Validi 32, Ufa 450074, Russia

A. A. Putintseva
Affiliation: Bashkir State University, Ul. Zaki Validi 32, Ufa 450074, Russia

P. C. Yulmukhametov
Affiliation: Institute of Mathematics with Computer Center, Ul. Chernyshevskogo 112, Ufa 450077, Russia

Keywords: Entire functions, Hilbert spaces, completeness and minimality for a system of exponentials, Fourier–Laplace transformation
Received by editor(s): June 17, 2009
Published electronically: June 27, 2011
Additional Notes: Supported by RFBR (grants nos. 08-01-97020-p_Volga_a, 10-01-00233-a)
Article copyright: © Copyright 2011 American Mathematical Society

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