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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 1, Pages 3–13 (Mi ivm8961)  
This article is cited in 1 scientific paper (total in 1 paper)

Linear continuous right inverse operator for convolution operator in spaces of holomorphic functions of polynomial growth

A. V. Abaninab, Le Hai Khoic

a Chair of Mathematical Analysis, Southern Federal University, 8-a Milchakov str., Rostov-on-Don, 344090 Russia
b Department of Mathematical Analysis, Southern Mathematical Institute
c Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
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Abstract: We consider a convolution operator in spaces of holomorphic functions in a convex domain of the complex plane with polynomial growth at a boundary. We proved that if this operator is surjective on the class of all bounded convex domains, then it always has a linear continuous right inverse operator.
Keywords: holomorphic function, polynomial growth, convolution operator, linear continuous right/left inverse operator.
Received: 30.07.2013
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, Volume 59, Issue 1, Pages 1–10
DOI: https://doi.org/10.3103/S1066369X15010016
Bibliographic databases:
Document Type: Article
UDC: 517.983
Language: Russian
Citation: A. V. Abanin, Le Hai Khoi, “Linear continuous right inverse operator for convolution operator in spaces of holomorphic functions of polynomial growth”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 1, 3–13; Russian Math. (Iz. VUZ), 59:1 (2015), 1–10
Citation in format AMSBIB
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\by A.~V.~Abanin, Le~Hai~Khoi
\paper Linear continuous right inverse operator for convolution operator in spaces of holomorphic functions of polynomial growth
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 1
\pages 3--13
\mathnet{http://mi.mathnet.ru/ivm8961}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 1
\pages 1--10
\crossref{https://doi.org/10.3103/S1066369X15010016}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84920838505}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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