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Mat. Zametki, 1976, Volume 19, Issue 5, Pages 691–698 (Mi mz7789)  

Approximation of Dirichlet polynomials in cases of sparse exponents

Z. Sh. Karimov

Bashkir State University

Abstract: Let $0<\lambda_k\uparrow\infty$, $\sum_{k=1}^\infty\lambda_k^{-1}<\infty$, and let $\gamma$ be an analytic arc. For the Dirichlet polynomial $P(z)=\sum_1^na_ke^\lambda k^z$, in angle $E-\pi/2+\varphi_0<\arg[-(z-a)]<\pi/2-\varphi_0$, $0<\varphi<\pi/2$, $\operatorname{Re}\alpha<\beta=\max\limits_{t\in\gamma}\operatorname{Re}t$ we obtain the estimate
$$ |P(z)|<A\max_{t\in\gamma}|P(t)|, $$
where $A$ depends only on angle $E$ $\{\lambda_k\}$. When $\gamma$ is a segment, an estimate was obtained by L. Schwartz.

Full text: PDF file (394 kB)

English version:
Mathematical Notes, 1976, 19:5, 415–419

Bibliographic databases:

UDC: 517.5
Received: 05.07.1974

Citation: Z. Sh. Karimov, “Approximation of Dirichlet polynomials in cases of sparse exponents”, Mat. Zametki, 19:5 (1976), 691–698; Math. Notes, 19:5 (1976), 415–419

Citation in format AMSBIB
\Bibitem{Kar76}
\by Z.~Sh.~Karimov
\paper Approximation of Dirichlet polynomials in cases of sparse exponents
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 5
\pages 691--698
\mathnet{http://mi.mathnet.ru/mz7789}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=430258}
\zmath{https://zbmath.org/?q=an:0343.30005}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 5
\pages 415--419
\crossref{https://doi.org/10.1007/BF01142562}


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