## Arkiv för Matematik

### Convolution operators in A−∞ for convex domains

#### Abstract

We consider the convolution operators in spaces of functions which are holomorphic in a bounded convex domain in ℂn and have a polynomial growth near its boundary. A characterization of the surjectivity of such operators on the class of all domains is given in terms of low bounds of the Laplace transformation of analytic functionals defining the operators.

#### Article information

Source
Ark. Mat., Volume 50, Number 1 (2012), 1-22.

Dates
Revised: 23 February 2011
First available in Project Euclid: 31 January 2017

https://projecteuclid.org/euclid.afm/1485907163

Digital Object Identifier
doi:10.1007/s11512-011-0146-4

Mathematical Reviews number (MathSciNet)
MR2890341

Zentralblatt MATH identifier
1254.32009

Rights

#### Citation

Abanin, Alexander V.; Ishimura, Ryuichi; Khoi, Le Hai. Convolution operators in A −∞ for convex domains. Ark. Mat. 50 (2012), no. 1, 1--22. doi:10.1007/s11512-011-0146-4. https://projecteuclid.org/euclid.afm/1485907163

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