Zeros of Generalized Holomorphic Functions

• Autores: A. Khelif, Dimitris Scarpalézos
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 149, Nº 4, 2006, págs. 323-335
• Idioma: inglés
• DOI: 10.1007/s00605-006-0393-9
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• Resumen

  • Let f be a generalized holomorphic function on a connected open set . It is proved that f equals zero if and only if there exists a smooth curve and a set A of positive (one-dimensional) measure such that f takes zero value on A. Also, a holomorphic generalized function different from zero on the disc, which takes zero values on a dense G d-set of the disc, is constructed. The generalized zero set of a holomorphic function is introduced and studied in an analogous way