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Sbornik: Mathematics, 2020, Volume 211, Issue 7, Pages 1014–1040
DOI: https://doi.org/10.1070/SM9183 (Mi sm9183) 		 
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
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DOI: https://doi.org/10.1070/SM9183
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
Russian version:
Matematicheskii Sbornik, 2020, Volume 211, Number 7, Pages 121–150
DOI: https://doi.org/10.4213/sm9183
Bibliographic databases:
Document Type: Article
UDC: 517.982.274+517.983.22
MSC: Primary 30H05, 34A35; Secondary 46A04, 46E10
Language: English
Original paper language: Russian
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”, Mat. Sb., 211:7 (2020), 121–150; Sb. Math., 211:7 (2020), 1014–1040
Citation in format AMSBIB
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    References:43
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