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Convolution of a Continuous Compact Support With a Polynomial is a Polynomial

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Abstract

We consider the convolution operator in spaces of holomorphic functions, defined in convex subdomains of the complex plane, with polynomial growth at a boundary. We prove that if this operator is surjective on the class of all bounded convex domains, then it always has a linear continuous right inverse one.

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Author information

Authors and Affiliations

  1. Southern Federal University, ul. Milchakova 8a, Rostov-on-Don, 344090, Russia

    A. V. Abanin

  2. Nanyang Technological University, 637371, Singapore, Singapore

    Le Hai Khoi

Corresponding author

Correspondence to A. V. Abanin.

Additional information

Original Russian Text © A.V. Abanin, Le Hai Khoi, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 1, pp. 3–13.

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Abanin, A.V., Khoi, L.H. Linear continuous right inverse to convolution operator in spaces of holomorphic functions of polynomial growth. Russ Math. 59, 1–10 (2015). https://doi.org/10.3103/S1066369X15010016

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  • DOI : https://doi.org/10.3103/S1066369X15010016

Keywords

  • holomorphic function
  • polynomial growth
  • convolution operator
  • linear continuous right/left inverse operator

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