Three equivalent conjectures on an estimate of integrals (in Russian)

Details Three equivalent conjectures on an estimate of integrals (in Russian) Three equivalent conjectures on an estimate of integrals (in Russian)

2010-06-26

arxiv.org/abs/1006.5140v1

Mathematics

Complex Variables

8 pages, submitted to Ufimskii Matematicheskii Zhurnal

Scientific paper

We offer a conjecture on sharp estimation of a definite improper integral depend on a parameter $\lambda \in (0,+\infty)$ by means of given estimate of other definite integral depend on parameters $t\in [0,+\infty)$ and $\lambda$. Such sharp estimate is proved for $\lambda \leq 1$. Besides, an estimate is obtained for $\lambda >1$. The last estimate is not exact seemingly. We give also two conjectures that are equivalent to the original conjecture. Sources of our conjectures are extremal problems for entire, meromorphic, and plurisubharmonic functions of several variables.

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