The Class of Holomorphic Functions Representable by Carleman Formula

Lev Aizenberg, Alexander Tumanov, Alekos Vidras

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Carleman formulas, unlike the Cauchy formula, restore a function holomorphic in a domain D by its values on a part M of the boundary ∂D, provided that M is of positive Lebesgue measure. Naturally arises the following question: Can we describe the class of holomorphic functions that are represented by Carleman formula? We consider the simplest Carleman formulas in one and several complex variables on very particular domains. Under these conditions the main result of the present paper is that a necessary and sufficient condition for a holomorphic function f to be represented by Carleman formula over the set M is that f must belong to "the class H1 near the set M " .

Original languageEnglish
Pages (from-to)93-105
Number of pages13
JournalAnnali della Scuola normale superiore di Pisa - Classe di scienze
Issue number1
StatePublished - 1998

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© 1998 Scuola Normale Superiore. All rights reserved.


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