On a class of holomorphic functions representable by Carleman formulas in the interior of an equilateral cone from their values on its rigid base |
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Authors: | George Chailos Alekos Vidras |
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Affiliation: | aDepartment of Computer Science, Intercollege, Nicosia 1700, Cyprus;bDepartment of Mathematics and Statistics, University of Cyprus, Nicosia 1678, Cyprus |
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Abstract: | Let Δ be an equilateral cone in C with vertices at the complex numbers and rigid base M (Section 1). Assume that the positive real semi-axis is the bisectrix of the angle at the origin. For the base M of the cone Δ we derive a Carleman formula representing all those holomorphic functions from their boundary values (if they exist) on M which belong to the class . The class is the class of holomorphic functions in Δ which belong to the Hardy class near the base M (Section 2). As an application of the above characterization, an important result is an extension theorem for a function fL1(M) to a function . |
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Keywords: | Carleman formula Cone with a rigid base |
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