Arkiv för Matematik

Convolution operators in A−∞ for convex domains

Alexander V. Abanin, Ryuichi Ishimura, and Le Hai Khoi

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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.

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

Received: 14 December 2009
Revised: 23 February 2011
First available in Project Euclid: 31 January 2017

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2011 © Institut Mittag-Leffler


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.

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