On extension theorems for holomorphic generalized functions

• Autor(a) principal: Soares, Marcelo Reicher [UNESP]
• Data de Publicação: 2009
• Tipo de documento: Artigo de conferência
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1080/10652460802568176; http://hdl.handle.net/11449/8603
• topic: holomorphic generalized functions; extension theorems; holomorphic on the boundary

We present two extension theorems for holomorphic generalized functions. The first one is a version of the classic Hartogs extension theorem. In this, we start from a holomorphic generalized function on an open neighbourhood of the bounded open boundary, extending it, holomorphically, to a full open. In the second theorem a generalized version of a classic result is obtained, done independently, in 1943, by Bochner and Severi. For this theorem, we start from a function that is holomorphic generalized and has a holomorphic representative on the bounded domain boundary, we extend it holomorphically the function, for the whole domain.