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 language||English (US)|
|Number of pages||13|
|Journal||Annali della Scuola Normale Superiore di Pisa - Classe di Scienze|
|State||Published - 1998|
ASJC Scopus subject areas
- Theoretical Computer Science
- Mathematics (miscellaneous)