Entire functions of sine type and their applications
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R. A. Bashmakov, A. A. Putintseva and P. C. Yulmukhametov
Translated by: S. Kislyakov - St. Petersburg Math. J. 22 (2011), 737-750
- DOI: https://doi.org/10.1090/S1061-0022-2011-01165-3
- Published electronically: June 27, 2011
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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.References
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Bibliographic Information
- R. A. Bashmakov
- Affiliation: Bashkir State University, Ul. Zaki Validi 32, Ufa 450074, Russia
- Email: bashmakov_rustem@mail.ru
- A. A. Putintseva
- Affiliation: Bashkir State University, Ul. Zaki Validi 32, Ufa 450074, Russia
- Email: PutinBSU@yandex.ru
- P. C. Yulmukhametov
- Affiliation: Institute of Mathematics with Computer Center, Ul. Chernyshevskogo 112, Ufa 450077, Russia
- Email: yulmukhametov@mail.ru
- 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)
- © Copyright 2011 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 737-750
- MSC (2010): Primary 30D15
- DOI: https://doi.org/10.1090/S1061-0022-2011-01165-3
- MathSciNet review: 2828826