Convolution operators in$A$^{−∞}for convex domains

Alexander V. Abanin Southern Institute of Mathematics, Southern Federal University Ryuichi Ishimura Graduate School of Science, Chiba University Le Hai Khoi Division of Mathematical Sciences School of Physical and Mathematical Sciences, Nanyang Technological University

Functional Analysis Spectral Theory and Operator Algebra mathscidoc:1701.12017

Arkiv for Matematik, 50, (1), 1-22, 2009.12
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.
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@inproceedings{alexander2009convolution,
  title={Convolution operators in$A$^{−∞}for convex domains},
  author={Alexander V. Abanin, Ryuichi Ishimura, and Le Hai Khoi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203631993466016},
  booktitle={Arkiv for Matematik},
  volume={50},
  number={1},
  pages={1-22},
  year={2009},
}
Alexander V. Abanin, Ryuichi Ishimura, and Le Hai Khoi. Convolution operators in$A$^{−∞}for convex domains. 2009. Vol. 50. In Arkiv for Matematik. pp.1-22. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203631993466016.
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