Generalized analytic functions on generalized domains

Details Generalized analytic functions on generalized domains Generalized analytic functions on generalized domains

2008-11-10

arxiv.org/abs/0811.1521v1

Mathematics

Functional Analysis

18 pages

Scientific paper

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.

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