Analytic solutions of convolution equations on convex sets with a mixed structure. I

S. N. Melikhov; L. V. Khanina

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arXiv · 1809.04473

Analytic solutions of convolution equations on convex sets with a mixed structure. I

S. N. Melikhov·L. V. Khanina

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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.

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S. N. Melikhov, L. V. Khanina. 2018-09-12. Analytic solutions of convolution equations on convex sets with a mixed structure. I. https://arxiv.org/abs/1809.04473

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