Convolution operators in A−∞ for convex domains

We consider the convolution operators in spaces of functions which are holomorphic in a bounded convex domain in ℂ n 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 tra...

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Bibliographic Details
Published in:Arkiv för matematik 2012-04, Vol.50 (1), p.1-22
Main Authors: Abanin, Alexander V., Ishimura, Ryuichi, Khoi, Le Hai
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We consider the convolution operators in spaces of functions which are holomorphic in a bounded convex domain in ℂ n 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.
ISSN:0004-2080
1871-2487
DOI:10.1007/s11512-011-0146-4