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Vladikavkaz. Mat. Zh., 2010, Volume 12, Number 3, Pages 3–20 (Mi vmj179)  

This article is cited in 5 scientific papers (total in 5 papers)

Division theorem in some weighted spaces of entire functions

A. V. Abaninab, D. A. Abaninaab

a Southern Federal University, Russia, Rostov-on-Don
b South Mathematical Institute of VSC RAS, Russia, Vladikavkaz

Abstract: We consider weighted spaces of entire functions which are dual to the Beurling spaces of ultradifferentiable functions of mean type. We prove a division theorem, which completely characterizes all divisors of these spaces. With the help of this theorem, we obtain a criterion for the solvability of convolution equations in the Beurling classes of mean type.

Key words: multiplication operator, division theorem, ultradifferentiable functions, convolution operator.

Full text: PDF file (220 kB)
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UDC: 517.547.2+517.982

Citation: A. V. Abanin, D. A. Abanina, “Division theorem in some weighted spaces of entire functions”, Vladikavkaz. Mat. Zh., 12:3 (2010), 3–20

Citation in format AMSBIB
\Bibitem{AbaPol10}
\by A.~V.~Abanin, D.~A.~Abanina
\paper Division theorem in some weighted spaces of entire functions
\jour Vladikavkaz. Mat. Zh.
\yr 2010
\vol 12
\issue 3
\pages 3--20
\mathnet{http://mi.mathnet.ru/vmj179}
\elib{https://elibrary.ru/item.asp?id=15181016}


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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. D. A. Abanina, “Representation of solutions of convolution equations in nonquasianalytic Beurling classes of ultradifferentiable functions of mean type”, Russian Math. (Iz. VUZ), 55:6 (2011), 1–8  mathnet  crossref  mathscinet  elib
    2. D. A. Abanina, “Solvability of convolution equations in the Beurling spaces of ultradifferentiable functions of mean type on an interval”, Siberian Math. J., 53:3 (2012), 377–392  mathnet  crossref  mathscinet  isi
    3. D. A. Abanina, A. V. Kuzminova, “O probleme deleniya v neradialnykh vesovykh prostranstvakh tselykh funktsii”, Vladikavk. matem. zhurn., 15:3 (2013), 7–18  mathnet
    4. D. A. Polyakova, “O chastnom reshenii neodnorodnogo uravneniya svertki v prostranstvakh ultradifferentsiruemykh funktsii”, Vladikavk. matem. zhurn., 20:4 (2018), 67–75  mathnet  crossref
    5. D. A. Polyakova, “General solution of homogeneous convolution equation in spaces of ultradifferentiable functions”, St. Petersburg Math. J., 31:1 (2020), 85–105  mathnet  crossref  isi  elib
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