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Mat. Zametki, 1976, Volume 19, Issue 2, Pages 225–236 (Mi mz7742)  

This article is cited in 1 scientific paper (total in 1 paper)

Solvability of partial differential equations of infinite order in certain classes of entire functions

G. G. Braichev


Abstract: In this paper it is shown that under conditions of applicability of the operator $\mathfrak Ly=\sum_{k\ge0}{a_kD^ky(x)}$ to the class $[\rho,\sigma]$, $\rho=(1,\rho_2$, $\rho_2<1$, $\sigma=(\sigma_1, \sigma_2)$, $\sigma_1,\sigma_2<\infty$ the equation $\mathfrak Ly=f$ has a particular solution of this class $\forall f\in[\rho,\sigma]$. The general form of a solution of the homogeneous equation $\mathfrak Ly=0$ is established. The growth of a solution is investigated by means of a system of conjugate orders and a system of conjugate types.
A solvability result is also obtained in the class $E(T)=\bigcup\limits_{\sigma\in T}[\rho,\sigma]$, where $T$ is a certain set in $R_+^2$ depending on the operator $\mathfrak L$.

Full text: PDF file (814 kB)

English version:
Mathematical Notes, 1976, 19:2, 135–140

Bibliographic databases:

UDC: 517.946
Received: 11.10.1974

Citation: G. G. Braichev, “Solvability of partial differential equations of infinite order in certain classes of entire functions”, Mat. Zametki, 19:2 (1976), 225–236; Math. Notes, 19:2 (1976), 135–140

Citation in format AMSBIB
\Bibitem{Bra76}
\by G.~G.~Braichev
\paper Solvability of partial differential equations of infinite order in certain classes of entire functions
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 2
\pages 225--236
\mathnet{http://mi.mathnet.ru/mz7742}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=417558}
\zmath{https://zbmath.org/?q=an:0326.35008}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 2
\pages 135--140
\crossref{https://doi.org/10.1007/BF01098746}


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    This publication is cited in the following articles:
    1. Yu. F. Korobeinik, “O primenenii teorii vozmuschenii normalno razreshimykh operatorov k nekotorym klassam operatorov v kompleksnoi oblasti”, Vladikavk. matem. zhurn., 7:2 (2005), 64–77  mathnet  mathscinet  elib
  • Математические заметки Mathematical Notes
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