Geodesic
Analytic solutions of convolution equations on convex sets in the complex plane with an open obstacle on the boundary
Sbornik. Mathematics, Tome 211 (2020) no. 7, pp. 1014-1040

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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: space of germs of analytic functions, continuous linear right inverse.
Mots-clés : convolution equation 
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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. Sbornik. Mathematics, Tome 211 (2020) no. 7, pp. 1014-1040. http://geodesic.mathdoc.fr/item/SM_2020_211_7_a5/