English

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.

Keywords

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}
}

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in Russian

R2 v1 2026-06-23T04:03:59.623Z