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Ufimskii Matematicheskii Zhurnal, 2010, Volume 2, Issue 3, Pages 31–38
(Mi ufa60)
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This article is cited in 2 scientific papers (total in 2 papers)
Three equivalent hypotheses on estimation of integrals
R. A. Baladai, B. N. Khabibullin Bashkir State University, Ufa, Russia
Abstract:
We offer a hypothesis on precise estimation of a definite improper integral depending on a parameter λ∈(0,+∞) by means of a given estimation of another definite integral depending on parameters t∈[0,+∞) and λ. This precise estimation is proved for λ≤1. Besides, an exact estimation is obtained for λ>1. The later estimation does not seem to be exact. We give two more hypotheses that are equivalent to the original one. Our conjectures originated from extreme problems for entire, meromorphic, and plurisubharmonic functions of several variables.
Keywords:
improper integral, estimate, inequality, entire function, meromorphic function, plurisubharmonic function, Paley problem.
Received: 15.06.2010
Citation:
R. A. Baladai, B. N. Khabibullin, “Three equivalent hypotheses on estimation of integrals”, Ufa Math. J., 2:3 (2010)
Linking options:
https://www.mathnet.ru/eng/ufa60 https://www.mathnet.ru/eng/ufa/v2/i3/p31
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Abstract page: | 560 | Full-text PDF : | 192 | References: | 102 | First page: | 2 |
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