Abstract
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 |
|---|---|
| Pages (from-to) | 93-105 |
| Number of pages | 13 |
| Journal | Annali della Scuola normale superiore di Pisa - Classe di scienze |
| Volume | 27 |
| Issue number | 1 |
| State | Published - 1998 |
Bibliographical note
Publisher Copyright:© 1998 Scuola Normale Superiore. All rights reserved.
Funding
(*) The author was supported by BSF Grant No.94-00113 (**) The author was supported by BSF Grant No.94-00113 (***) The author was supported by a Grant of Univ. of Cyprus Pervenuto alla Redazione il 20 gennaio 1998 e in forma definitiva il 28 maggio 1998.
| Funders | Funder number |
|---|---|
| United States-Israel Binational Science Foundation |