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Izv. Vyssh. Uchebn. Zaved. Mat., 2015, Number 1, Pages 3–13 (Mi ivm8961)  

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

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.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:1, 1–10

UDC: 517.983
Received: 30.07.2013

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
\Bibitem{AbaKho15}
\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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84920838505}


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