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Mat. Zametki, 1976, Volume 19, Issue 1, Pages 19–28 (Mi mz7719)  

Extremal problems in a subclass of entire functions of finite power

S. A. Kas'yanyuk


Abstract: We study the subclass $W_\sigma(A)$ of the class of entire transcendental functions $f(z)$of exponential type with index not greater than sgr satisfying the condition
$$ \int_{-\infty}^\infty|f(x)|^2 dx\le A^2 $$
We find the set of values of the quantities $f(z)$, $f'(z)$, etc. when $z$ is fixed and $f(z)$ runs through the subclass $W_\sigma(A)$. We study extremal values of functionals of the type $\Phi(f(z),f'(z))$. In particular, we obtain upper bounds on the quantities $|f(z+\beta/2)\pm f(z-\beta/2)|$ и $|af'(z)+b\sigma f(z)|$.

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English version:
Mathematical Notes, 1976, 19:1, 11–16

Bibliographic databases:

UDC: 517.5
Received: 06.11.1974

Citation: S. A. Kas'yanyuk, “Extremal problems in a subclass of entire functions of finite power”, Mat. Zametki, 19:1 (1976), 19–28; Math. Notes, 19:1 (1976), 11–16

Citation in format AMSBIB
\Bibitem{Kas76}
\by S.~A.~Kas'yanyuk
\paper Extremal problems in a~subclass of entire functions of finite power
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 1
\pages 19--28
\mathnet{http://mi.mathnet.ru/mz7719}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=407278}
\zmath{https://zbmath.org/?q=an:0331.30024|0329.30016}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 1
\pages 11--16
\crossref{https://doi.org/10.1007/BF01147611}


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