Some inequalities for entire functions
Анотація
Let Lp be the subspace of the space Lp(R) consisting of the restriction to the real axis of all entire functions of exponential type ≤π. In this paper, for any function f∈Lp(1≤p≤∞), we obtain estimates for the norm of f in terms of the sequence (f(n/2))n∈Z, namely
12‖f‖p,1≤‖f‖Lp≤2‖f‖p,1,
where ‖f‖p,1:=12(‖Jf‖ℓp(Z)+‖JT1/2f‖ℓp(Z)). Here J:Lp→ℓp(Z) is the linear operator given by the formula (Jf)(n):=(−1)nf(n),n∈Z, and Tτ is the shift by τ∈R of the function f,
(Tτf)(z):=f(z+τ),z∈C.
Посилання
B.Ya. Levin, Lectures on entire functions, Translations of Mathematical Monographs, V.150, AMS, Providence, RI, 1996.
I.S. Gradshteyn, I.M. Ryzhik, Table of integrals, series, and products, Academic Press, Editors: Daniel Zwillinger, Victor Moll, 2014. doi.org/10.1016/C2010-0-64839-5
Авторське право (c) 2024 D. Lukivska, N. Sushchyk

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