arXiv subjects

L. V. Khanina

Publications and source records attributed to L. V. Khanina.

2 recordsLinked to original sources

arXiv2018

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

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.

math.FA↗

arXiv2018

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

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.

math.FA↗