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 Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 5, Pages 1124–1136 (Mi izv983)

Differential operators of infinite order with symbols of Gevrey class

O. V. Odinokov

Abstract: Differential operators of infinite order with symbols that are infinitely differentiable functions (of Gevrey class) in some domain in $\mathbf R^n$ are considered. With the help of such operators a generalized Fourier transform of infinitely differentiable functions is constructed. For these operators a criterion for the of solvability of the Cauchy problem in some subclasses of exponential functions is proved. The results are similar to those of Dubinskii [1] for differential operators of infinite order with symbols analytic in some Runge domain in $\mathbf C^n$.

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English version:
Mathematics of the USSR-Izvestiya, 1992, 39:2, 1085–1096

Bibliographic databases:

UDC: 517.955.2+517.547
MSC: 35R50, 47F05

Citation: O. V. Odinokov, “Differential operators of infinite order with symbols of Gevrey class”, Izv. Akad. Nauk SSSR Ser. Mat., 55:5 (1991), 1124–1136; Math. USSR-Izv., 39:2 (1992), 1085–1096

Citation in format AMSBIB
\Bibitem{Odi91} \by O.~V.~Odinokov \paper Differential operators of infinite order with symbols of Gevrey class \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1991 \vol 55 \issue 5 \pages 1124--1136 \mathnet{http://mi.mathnet.ru/izv983} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1149890} \zmath{https://zbmath.org/?q=an:0777.47027} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992IzMat..39.1085O} \transl \jour Math. USSR-Izv. \yr 1992 \vol 39 \issue 2 \pages 1085--1096 \crossref{https://doi.org/10.1070/IM1992v039n02ABEH002238} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992JZ92300007} 

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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, “Differential operators of infinite order in some spaces of entire functions”, Russian Acad. Sci. Izv. Math., 43:2 (1994), 347–361
2. O. V. Odinokov, “Integral representation of entire functions and differential operators of infinite order”, Izv. Math., 59:4 (1995), 839–846
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