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Mat. Sb., 1993, Volume 184, Number 8, Pages 81–108 (Mi msb1006)  

This article is cited in 10 scientific papers (total in 10 papers)

On indicators of entire functions and extension of solutions of a homogeneous convolution equation

A. S. Krivosheev

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

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.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 79:2, 401–423

Bibliographic databases:

UDC: 517.55
MSC: Primary 32D99, 44A35; Secondary 32A22, 44A10, 32F05
Received: 30.01.1992

Citation: A. S. Krivosheev, “On indicators of entire functions and extension of solutions of a homogeneous convolution equation”, Mat. Sb., 184:8 (1993), 81–108; Russian Acad. Sci. Sb. Math., 79:2 (1994), 401–423

Citation in format AMSBIB
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\by A.~S.~Krivosheev
\paper On indicators of entire functions and extension of solutions of a~homogeneous convolution equation
\jour Mat. Sb.
\yr 1993
\vol 184
\issue 8
\pages 81--108
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1239760}
\zmath{https://zbmath.org/?q=an:0842.32003}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 79
\issue 2
\pages 401--423
\crossref{https://doi.org/10.1070/SM1994v079n02ABEH003507}
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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. A. S. Krivosheev, “Analytic continuation of functions from invariant subspaces in convex domains of the complex space”, Izv. Math., 62:2 (1998), 287–312  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Krivosheev A., “Analytic Continuation of Functions From Invariant Subspaces”, Dokl. Math., 66:2 (2002), 217–219  mathscinet  zmath  isi
    3. I. F. Krasichkov-Ternovskii, “Spectral synthesis and analytic continuation”, Russian Math. Surveys, 58:1 (2003), 31–108  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. 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  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. A. S. Krivosheev, “A fundamental principle for invariant subspaces in convex domains”, Izv. Math., 68:2 (2004), 291–353  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Krivosheev A.S., “Continuation of Functions From Principal Invariant Subspaces”, Dokl. Math., 74:2 (2006), 728–730  crossref  mathscinet  zmath  isi  elib
    7. A. S. Krivosheev, “Invariantnye podprostranstva v vypuklykh oblastyakh iz $\mathbb C^n$”, Ufimsk. matem. zhurn., 1:2 (2009), 53–74  mathnet  zmath  elib
    8. A. S. Krivosheev, “Invariantnye podprostranstva v vypuklykh oblastyakh iz $\mathbb C^n$”, Ufimsk. matem. zhurn., 1:3 (2009), 65–86  mathnet  zmath  elib
    9. A. S. Krivosheev, “Criterion of analytic continuability of functions in principal invariant subspaces on convex domains in $\mathbb C^n$”, St. Petersburg Math. J., 22:4 (2011), 615–655  mathnet  crossref  mathscinet  zmath  isi
    10. A. S. Krivosheev, O. A. Krivosheyeva, “A basis in invariant subspace of entire functions”, St. Petersburg Math. J., 27:2 (2016), 273–316  mathnet  crossref  mathscinet  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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