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Mat. Zametki, 1976, Volume 19, Issue 2, Pages 215–224 (Mi mz7741)  

A class of weighted spaces of entire functions

V. A. Bogachev

Rostov State University

Abstract: In the class of weighted spaces of entire functions
$$ B_{\Phi(x,y)}=\{f(z)\in A_\infty:\sup_{z\in C}\frac{|f(z)|}{\Phi(x,y)}<\infty\}\quad(z=x+iy), $$
where $\Phi(x,y)$ is a continuous function on $R^2$ possessing certain additional properties, estimates are obtained for the norms of derivatives and norms of functions involving a translation of the independent variable in terms of the norm of the original function. These estimates are then used to prove the existence and uniqueness of solutions in the spaces $B_{\Phi(x,y)}$ of linear differential-difference equations of infinite order with constant coefficients.

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English version:
Mathematical Notes, 1976, 19:2, 129–134

Bibliographic databases:

UDC: 517.9
Received: 20.03.1975

Citation: V. A. Bogachev, “A class of weighted spaces of entire functions”, Mat. Zametki, 19:2 (1976), 215–224; Math. Notes, 19:2 (1976), 129–134

Citation in format AMSBIB
\Bibitem{Bog76}
\by V.~A.~Bogachev
\paper A~class of weighted spaces of entire functions
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 2
\pages 215--224
\mathnet{http://mi.mathnet.ru/mz7741}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=412438}
\zmath{https://zbmath.org/?q=an:0359.34011|0352.34011}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 2
\pages 129--134
\crossref{https://doi.org/10.1007/BF01098745}


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