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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 4, Pages 179–186 (Mi izv36)  

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

Integral representation of entire functions and differential operators of infinite order

O. V. Odinokov


Abstract: In this article we derive an integral representation in certain spaces of entire functions of exponential type in $\mathbb C^n$. To this end we use the isomorphism, given by the Laplace operator, between these spaces and the corresponding spaces of ultradistributions. Using this integral representation these functions admit a well-defined action of differential operators of infinite order with specific conditions on the characteristic function.

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English version:
Izvestiya: Mathematics, 1995, 59:4, 839–846

Bibliographic databases:

MSC: 35R50, 30D10, 32A25, 32A15
Received: 30.05.1994

Citation: O. V. Odinokov, “Integral representation of entire functions and differential operators of infinite order”, Izv. RAN. Ser. Mat., 59:4 (1995), 179–186; Izv. Math., 59:4 (1995), 839–846

Citation in format AMSBIB
\Bibitem{Odi95}
\by O.~V.~Odinokov
\paper Integral representation of entire functions and differential operators of infinite order
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 4
\pages 179--186
\mathnet{http://mi.mathnet.ru/izv36}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1356355}
\zmath{https://zbmath.org/?q=an:0871.32002}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 4
\pages 839--846
\crossref{https://doi.org/10.1070/IM1995v059n04ABEH000036}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000169556400009}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. V. Odinokov, “Spectral synthesis in certain spaces of entire functions of exponential type and its applications”, Izv. Math., 64:4 (2000), 777–786  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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