The class of holomorphic functions representable by Carleman formula

• Lev Aizenberg ^[1] ; Alexander Tumanov ^[3] ; Alekos Vidras ^[2]
  1. [1] Bar-Ilan University

     Bar-Ilan University

     Israel

     
  2. [2] University of Cyprus

     University of Cyprus

     Chipre

     
  3. [3] University of Illinois, USA

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 27, Nº 1, 1998, págs. 93-105
• Idioma: inglés
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• Resumen

  • Carleman formulas, unlike the Cauchy formula, restore a function holomorphic in a domain D by its values on a part M of the boundary aD, 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 1i near the set M".