Linear continuous right inverse to convolution operator in spaces of holomorphic functions of polynomial growth. (English. Russian original) Zbl 1319.30047

Abanin, A. V.; Khoi, Le Hai

Russ. Math. 59, No. 1, 1-10 (2015); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2015, No. 1, 3-13 (2015).

Summary: 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.

MSC:

30H99

Spaces and algebras of analytic functions of one complex variable

Keywords:

spaces of holomorphic functions; convolution operator

References:

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