Abstract:
A study is made of the problem of extending solutions of a homogeneous convolution equation generated by analytic functional on convex domains in a multidimensional complex space. Conditions ensuring the simultaneous extension of solutions are given in terms of complete regularity of the growth in limiting directions of accumulations of zeros of the Laplace transform of an analytic functional. These conditions generalize previously known results on this problem. Some properties of indicators of entire functions are also presented.
Citation:
A. S. Krivosheev, “On indicators of entire functions and extension of solutions of a homogeneous convolution equation”, Russian Acad. Sci. Sb. Math., 79:2 (1994), 401–423
\Bibitem{Kri93}
\by A.~S.~Krivosheev
\paper On indicators of entire functions and extension of solutions of a~homogeneous convolution equation
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 79
\issue 2
\pages 401--423
\mathnet{http://mi.mathnet.ru/eng/sm1006}
\crossref{https://doi.org/10.1070/SM1994v079n02ABEH003507}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1239760}
\zmath{https://zbmath.org/?q=an:0842.32003}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994PY27400010}
Linking options:
https://www.mathnet.ru/eng/sm1006
https://doi.org/10.1070/SM1994v079n02ABEH003507
https://www.mathnet.ru/eng/sm/v184/i8/p81
This publication is cited in the following 11 articles:
A. S. Krivosheev, O. A. Krivosheeva, “Necessary condition of fundamental principle for invariant subspaces on unbounded convex domain”, Ufa Math. J., 15:3 (2023), 69–79
A. S. Krivosheev, O. A. Krivosheyeva, “A basis in invariant subspace of entire functions”, St. Petersburg Math. J., 27:2 (2016), 273–316
A. S. Krivosheev, “Criterion of analytic continuability of functions in principal invariant subspaces on convex domains in Cn”, St. Petersburg Math. J., 22:4 (2011), 615–655
A. S. Krivosheev, “Invariantnye podprostranstva v vypuklykh oblastyakh iz Cn”, Ufimsk. matem. zhurn., 1:2 (2009), 53–74
A. S. Krivosheev, “Invariantnye podprostranstva v vypuklykh oblastyakh iz Cn”, Ufimsk. matem. zhurn., 1:3 (2009), 65–86
Krivosheev A.S., “Continuation of Functions From Principal Invariant Subspaces”, Dokl. Math., 74:2 (2006), 728–730
A. S. Krivosheev, “A criterion for analytic continuation of functions from invariant subspaces in convex domains of the complex plane”, Izv. Math., 68:1 (2004), 43–76
A. S. Krivosheev, “A fundamental principle for invariant subspaces in convex domains”, Izv. Math., 68:2 (2004), 291–353
I. F. Krasichkov-Ternovskii, “Spectral synthesis and analytic continuation”, Russian Math. Surveys, 58:1 (2003), 31–108
Krivosheev A., “Analytic Continuation of Functions From Invariant Subspaces”, Dokl. Math., 66:2 (2002), 217–219
A. S. Krivosheev, “Analytic continuation of functions from invariant subspaces in convex domains of the complex space”, Izv. Math., 62:2 (1998), 287–312
Citation in format AMSBIB
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