Analytic solutions of convolution equations on convex sets with a mixed structure. II
Functional Analysis
2018-10-22 v2
Abstract
We prove conditions for the existence of a continuous linear right inverse for a surjective convolution operator in spaces of germs of analytic functions on convex subsets of the complex plane. Considered convex sets have a countable neighborhood basis of convex domains. Mentioned conditions are obtained in terms of the boundary behavior of convex univalent functions which are defined by these sets.
Cite
@article{arxiv.1810.02625,
title = {Analytic solutions of convolution equations on convex sets with a mixed structure. II},
author = {S. N. Melikhov and L. V. Khanina},
journal= {arXiv preprint arXiv:1810.02625},
year = {2018}
}
Comments
in Russian. This is the second part of our article arXiv:1809.04473