Point value characterizations and related results in the full Colombeau algebras G^e and G^d
Eduard Nigsch
TL;DR
This paper provides point value characterizations for elements in the full Colombeau algebras G^e and G^d, extending known results from the special algebra G^s to these more general frameworks.
Contribution
It introduces point value characterizations for G^e and G^d and extends results on generalized numbers and invertibility from G^s to these full algebras.
Findings
Point value characterization for G^e and G^d.
Extension of generalized number results to G^e and G^d.
Results on invertibility in full Colombeau algebras.
Abstract
We present a point value characterization for elements of the elementary full Colombeau algebra G^e and the diffeomorphism invariant full Colombeau algebra G^d. Moreover, several results from the special algebra G^s about generalized numbers and invertibility are extended to the elementary full algebra.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Mathematical Analysis and Transform Methods · Advanced Topology and Set Theory