Analytic solutions of convolution equations on convex sets with a mixed structure. I
Functional Analysis
2018-10-22 v3
Abstract
We prove an abstract criterion that a surjective convolution operator in spaces of analytic functions on convex subsets of the complex plane has a continuous linear right inverse. Considered convex sets have a countable neighborhood basis of convex domains. The mentioned criterion is obtained in terms of the existence of a special family of subharmonic functions with global upper bounds and local lower bounds.
Cite
@article{arxiv.1809.04473,
title = {Analytic solutions of convolution equations on convex sets with a mixed structure. I},
author = {S. N. Melikhov and L. V. Khanina},
journal= {arXiv preprint arXiv:1809.04473},
year = {2018}
}
Comments
in Russian