Global Representatives of Colombeau Holomorphic Generalized Functions

• Autores: Michael Oberguggenberger, Stevan Pilipovic, V Valmorin
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 151, Nº 1, 2007, págs. 67-74
• Idioma: inglés
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• Resumen

  • It is proved that a holomorphic generalized function in the sense of Colombeau has a representative consisting of a net of holomorphic functions. More generally, the existence of global representatives of Colombeau solutions to elliptic partial differential equations is proved. Further, it is shown that a generalized holomorphic function on O, which is equal to zero in an open set , is equal to zero.