2008/11/10 by Hans Vernaeve, Vernaeve, Hans
Mathematics · #46F30 #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis #math.FA #msc:46F30
paper · pdf · doi:10.48550/arxiv.0811.1521
18 pages
arxiv created 2008/11/10 · openalex publication_date 2008/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the algebra of Colombeau generalized functions on a subset A of the space of d-dimensional generalized points. If the domain A is open, such generalized functions can be identified with pointwise maps from A into the ring of Colombeau generalized numbers. We study analyticity in these algebras, if the domain is an open subset of the complex generalized points. In particular, if the domain is an open ball for the sharp norm, we characterize analyticity and give a unicity theorem involving the values at generalized points.