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Izv. RAN. Ser. Mat., 1997, Volume 61, Issue 3, Pages 91–132 (Mi izv127)  

This article is cited in 8 scientific papers (total in 8 papers)

Representative systems of exponentials and the Cauchy problem for partial differential equations with constant coefficients

Yu. F. Korobeinik

Rostov State University

Abstract: We consider the Cauchy problem with respect to $z_2$ for a homogeneous linear partial differential equation with constant coefficients in two independent variables $z_1,z_2 \in \mathbb C$. We show that the relative smoothness with respect to $z_1$ and $z_2$ of analytic and ultradifferentiable solutions of the Cauchy problem depends essentially on the value of $\rho_2$ and, as a rule, is completely determined by it. We also obtain rather general uniqueness theorems and find conditions which guarantee that the particular solution constructed depends both continuously and linearly on the initial functions.

DOI: https://doi.org/10.4213/im127

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English version:
Izvestiya: Mathematics, 1997, 61:3, 553–592

Bibliographic databases:

MSC: 35E15, 46E10
Received: 15.02.1995

Citation: Yu. F. Korobeinik, “Representative systems of exponentials and the Cauchy problem for partial differential equations with constant coefficients”, Izv. RAN. Ser. Mat., 61:3 (1997), 91–132; Izv. Math., 61:3 (1997), 553–592

Citation in format AMSBIB
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\by Yu.~F.~Korobeinik
\paper Representative systems of exponentials and the Cauchy problem for partial differential equations with constant coefficients
\jour Izv. RAN. Ser. Mat.
\yr 1997
\vol 61
\issue 3
\pages 91--132
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\transl
\jour Izv. Math.
\yr 1997
\vol 61
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\pages 553--592
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    Citing articles on Google Scholar: Russian citations, English citations
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    Erratum

    This publication is cited in the following articles:
    1. Yu. F. Korobeinik, “Letter to the Editors”, Izv. Math., 62:3 (1998), 649–649  mathnet  crossref  crossref  mathscinet  isi
    2. Korobeinik Y.F., “The Fourier method in the Cauchy problem and absolutely representing systems of exponentials. I”, Differential Equations, 35:12 (1999), 1693–1701  mathnet  mathscinet  zmath  isi  elib
    3. Korobeinik Y.F., “Absolutely representing systems of exponentials with imaginary exponents in spaces of infinitely differentiable functions”, Doklady Mathematics, 61:3 (2000), 324–327  mathscinet  zmath  isi  elib
    4. Korobeinik Y.F., “On absolutely representing systems in spaces of infinitely differentiable functions”, Studia Mathematica, 139:2 (2000), 175–188  crossref  mathscinet  zmath  isi  elib
    5. Korobeinik Y.F., “The Fourier method in the Cauchy problem and absolutely representing systems of exponentials: III”, Differential Equations, 36:3 (2000), 433–440  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. Korobeinik Y.F., “The Fourier method in the Cauchy problem and absolutely representing systems of exponentials: II”, Differential Equations, 36:2 (2000), 285–290  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. Alexander A. Znamenskiy, “A refinement of Kovalevskaya's theorem on analytic solvability of the Cauchy problem”, Zhurn. SFU. Ser. Matem. i fiz., 10:4 (2017), 531–536  mathnet  crossref
    8. S. N. Melikhov, “Koeffitsienty ryadov eksponent dlya analiticheskikh funktsii i operator Pomme”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 65–103  mathnet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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