Arkiv för Matematik

Convolution operators in A−∞ for convex domains

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

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

Permanent link to this document
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
2011 © Institut Mittag-Leffler

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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