Page 1

Displaying 1 – 4 of 4

Showing per page

Recent progress in special Colombeau algebras: geometry, topology, and algebra

M. Kunzinger (2010)

Banach Center Publications

Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of modules over the ring of generalized numbers, and algebraic aspects of Colombeau theory. Some open problems are given and directions of further research are outlined.

Results on generalized models and singular products of distributions in the Colombeau algebra 𝒢 ( )

Blagovest Damyanov (2015)

Commentationes Mathematicae Universitatis Carolinae

Models of singularities given by discontinuous functions or distributions by means of generalized functions of Colombeau have proved useful in many problems posed by physical phenomena. In this paper, we introduce in a systematic way generalized functions that model singularities given by distributions with singular point support. Furthermore, we evaluate various products of such generalized models when the results admit associated distributions. The obtained results follow the idea of a well-known...

Currently displaying 1 – 4 of 4

Page 1