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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 2, Pages 378–392 (Mi izv1810)  

This article is cited in 12 scientific papers (total in 12 papers)

Equations of convolution type in spaces of analytic functionals

V. A. Tkachenko


Abstract: In this work necessary and sufficient conditions are obtained for solvability of the equation $\Phi^*f=g$, where $\Phi^*$ is the adjoint of the operator of multiplication by an entire function of normal type with a finite order of growth. As an application some conditions are found for solvability of a nonhomogeneous equation of generalized convolution type.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:2, 361–374

Bibliographic databases:

UDC: 517.9
MSC: Primary 45E10, 46F15; Secondary 30A64, 44A15
Received: 29.01.1975

Citation: V. A. Tkachenko, “Equations of convolution type in spaces of analytic functionals”, Izv. Akad. Nauk SSSR Ser. Mat., 41:2 (1977), 378–392; Math. USSR-Izv., 11:2 (1977), 361–374

Citation in format AMSBIB
\Bibitem{Tka77}
\by V.~A.~Tkachenko
\paper Equations of convolution type in spaces of analytic functionals
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 2
\pages 378--392
\mathnet{http://mi.mathnet.ru/izv1810}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=487445}
\zmath{https://zbmath.org/?q=an:0356.45006|0378.45004}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 2
\pages 361--374
\crossref{https://doi.org/10.1070/IM1977v011n02ABEH001722}


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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. S. A. Apresyan, “Localization of ideals and asymptotic uniqueness theorems for functions with restrictions on growth”, Math. USSR-Sb., 34:5 (1978), 561–592  mathnet  crossref  mathscinet  zmath
    2. O. V. Epifanov, “Multiplication operators in spaces of entire functions of finite order and operators of convolution type”, Math. USSR-Sb., 48:2 (1984), 499–520  mathnet  crossref  mathscinet  zmath
    3. V. V. Morzhakov, “On epimorphicity of a convolution operator in convex domains in $\mathbf C^l$”, Math. USSR-Sb., 60:2 (1988), 347–364  mathnet  crossref  mathscinet  zmath
    4. Yu. F. Korobeinik, “Description of the general form of nontrivial expansions of zero in exponentials. Applications”, Math. USSR-Izv., 39:2 (1992), 1013–1032  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. B. N. Khabibullin, “Balayage on a system of rays and entire functions of completely regular growth”, Math. USSR-Izv., 38:1 (1992), 179–197  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Yu. F. Korobeinik, “Nontrivial expansions of zero in absolutely representing systems. Application to convolution operators”, Math. USSR-Sb., 73:1 (1992), 49–66  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. A. B. Shishkin, “Spectral synthesis for an operator generated by multiplication by a power of the independent variable”, Math. USSR-Sb., 73:1 (1992), 211–229  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. Yu. F. Korobeinik, “Representative systems of exponentials and the Cauchy problem for partial differential equations with constant coefficients”, Izv. Math., 61:3 (1997), 553–592  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. A. V. Abanin, “Ob odnom primenenii slabo dostatochnykh mnozhestv”, Vladikavk. matem. zhurn., 7:2 (2005), 11–16  mathnet  mathscinet  elib
    10. A. V. Abanin, D. A. Abanina, “Teorema deleniya v nekotorykh vesovykh prostranstvakh tselykh funktsii”, Vladikavk. matem. zhurn., 12:3 (2010), 3–20  mathnet  elib
    11. Abanin A.V. Ishimura R. Khoi L.H., “Convolution Operators in a(-Infinity) for Convex Domains”, Ark. Mat., 50:1 (2012), 1–22  crossref  isi
    12. D. A. Abanina, A. V. Kuzminova, “O probleme deleniya v neradialnykh vesovykh prostranstvakh tselykh funktsii”, Vladikavk. matem. zhurn., 15:3 (2013), 7–18  mathnet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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