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Analytic solutions of convolution equations on convex sets in the complex plane with an open obstacle on the boundary
S. N. Melikhovab, L. V. Khaninaa a Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, Rostov-on-Don
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
Abstract:
Conditions, including criteria, are established for the existence of a continuous linear right inverse to a surjective convolution operator in the space of germs of analytic functions on a convex subset of the complex plane which has a countable neighbourhood basis consisting of convex domains. These are stated in terms of the existence of special families of subharmonic functions and the boundary behaviour of convex conformal mappings related to the sets in question.
Bibliography: 50 titles.
Keywords:
convolution equation, space of germs of analytic functions, continuous linear right inverse.
Received: 19.10.2018 and 30.04.2020
Citation:
S. N. Melikhov, L. V. Khanina, “Analytic solutions of convolution equations on convex sets in the complex plane with an open obstacle on the boundary”, Sb. Math., 211:7 (2020), 1014–1040
Linking options:
https://www.mathnet.ru/eng/sm9183https://doi.org/10.1070/SM9183 https://www.mathnet.ru/eng/sm/v211/i7/p121
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