Displaying similar documents to “Singularities and normal forms of generic 2-distributions on 3-manifolds”

On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)

Damyanov, Blagovest P. (2013)

Mathematica Balkanica New Series

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MSC 2010: 46F30, 46F10 Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of Colombeau that model such singularities. Moreover, we evaluate some products of singularity-modelling generalized functions whenever the result admits an associated distribution.

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

Blagovest Damyanov (2015)

Commentationes Mathematicae Universitatis Carolinae

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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...

The elementary theory of distributions (I)

Jan Mikusiński, Roman Sikorski

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CONTENTS Introduction........................................................................................................... 3 § 1. The abstraction principle............................................................................... 4 § 2. Fundamental sequences of continuous functions......................................... 5 § 3. The definition of distributions........................................................................ 9 § 4. Distributions as a generalization of...