Abstract
Let be a bounded, simply connected domain with Jordan rectifiable boundary and let be an open analytic arc whose Lebesgue measure satisfies . Our result gives a complete description of the class of holomorphic functions in which are represented by the Carleman formulas on the open arc M, when is almost regular with respect to M (Section 2). That is, we give a type of integral representation formulas for functions holomorphic in a domain by its values on a part M of the boundary . This class is denoted by
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