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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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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