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Izv. RAN. Ser. Mat., 2000, Volume 64, Issue 4, Pages 131–140 (Mi izv297)  

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

Spectral synthesis in certain spaces of entire functions of exponential type and its applications

O. V. Odinokov


Abstract: We consider certain spaces $P_\Omega$ of entire functions of exponential type in $\mathbb C^n$ associated with a domain $\Omega\in\mathbb R^n$ that are in fact Laplace transforms of distributions in $\Omega$. It is shown that any shift-invariant subspace of these functions admits spectral synthesis, that is, coincides with the closure of the linear span of the exponential polynomials contained in it. As an application of this result, we describe the solution space in $P_\Omega$ of a system of homogeneous equations of infinite order for differential operators with characteristic functions infinitely differentiable in $\Omega$.

DOI: https://doi.org/10.4213/im297

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English version:
Izvestiya: Mathematics, 2000, 64:4, 777–786

Bibliographic databases:

MSC: 30D10, 32A15, 32A25, 35G05, 35R50, 42A38
Received: 15.05.1999

Citation: O. V. Odinokov, “Spectral synthesis in certain spaces of entire functions of exponential type and its applications”, Izv. RAN. Ser. Mat., 64:4 (2000), 131–140; Izv. Math., 64:4 (2000), 777–786

Citation in format AMSBIB
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\pages 131--140
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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