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Sibirsk. Mat. Zh., 2012, Volume 53, Number 3, Pages 477–494 (Mi smj2340)  

This article is cited in 6 scientific papers (total in 6 papers)

Solvability of convolution equations in the Beurling spaces of ultradifferentiable functions of mean type on an interval

D. A. Abaninaab

a Southern Federal University, Faculty of Mathematics, Mechanics and Computer Sciences, Rostov-on-Don
b South Mathematical Institute of VSC RAS, Vladikavkaz

Abstract: We establish a solvability criterion for convolution equations in the Beurling classes of ultradifferentiable functions of mean type on an interval. Under study is also the question of degeneration of convolution equations into infinite-order equations with constant coefficients.

Keywords: ultradifferentiable functions, convolution equation, division theorem.

Full text: PDF file (356 kB)
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English version:
Siberian Mathematical Journal, 2012, 53:3, 377–392

Bibliographic databases:

UDC: 517.983+517.5
Received: 15.06.2011

Citation: D. A. Abanina, “Solvability of convolution equations in the Beurling spaces of ultradifferentiable functions of mean type on an interval”, Sibirsk. Mat. Zh., 53:3 (2012), 477–494; Siberian Math. J., 53:3 (2012), 377–392

Citation in format AMSBIB
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\by D.~A.~Abanina
\paper Solvability of convolution equations in the Beurling spaces of ultradifferentiable functions of mean type on an interval
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 3
\pages 477--494
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\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 3
\pages 377--392
\crossref{https://doi.org/10.1134/S0037446612020206}
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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. Abanina D.A., “O suschestvovanii resheniya uravneniya svertki, lineino i nepreryvno zavisyaschego ot pravoi chasti”, Izvestiya vysshikh uchebnykh zavedenii. severo-kavkazskii region. seriya: estestvennye nauki, 2012, no. 6, 13–15  elib
    2. D. A. Abanina, A. V. Kuzminova, “O probleme deleniya v neradialnykh vesovykh prostranstvakh tselykh funktsii”, Vladikavk. matem. zhurn., 15:3 (2013), 7–18  mathnet
    3. D. A. Polyakova, “On the Continuous Linear Right Inverse for Convolution Operators in Spaces of Ultradifferentiable Functions”, Math. Notes, 96:4 (2014), 522–537  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. D. A. Polyakova, “On solutions of convolution equations in spaces of ultradifferentiable functions”, St. Petersburg Math. J., 26:6 (2015), 949–963  mathnet  crossref  mathscinet  isi  elib  elib
    5. D. A. Polyakova, “On generators of spaces of entire functions with a system of weighted estimates”, J. Math. Sci. (N. Y.), 229:5 (2018), 545–560  mathnet  crossref  mathscinet
    6. D. A. Polyakova, “Solvability of the inhomogeneous Cauchy–Riemann equation in projective weighted spaces”, Siberian Math. J., 58:1 (2017), 142–152  mathnet  crossref  crossref  isi  elib  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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