On a class of holomorphic functions representable by Carleman formulas in some class of bounded, simply connected domains from their values on an analytic arc
Date
2006Source
Monatshefte fur MathematikVolume
149Issue
4Pages
289-301Google Scholar check
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Let sript U sign be a bounded, simply connected domain with Jordan rectifiable boundary and let M ⊂ ∂ sript U sign be an open analytic arc whose Lebesgue measure satisfies 0 < m(M) < m(∂ sript U sign. Our result gives a complete description of the class of holomorphic functions in sript U sign which are represented by the Carleman formulas on the open arc M, when ∂ sript U sign 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 sript U sign by its values on a part M of the boundary ∂ sript U sign. This class is denoted by sript N sign ℋ1 M(sript U sign). © Springer-Verlag 2006.