All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3

Displaying 41 – 53 of 53

Showing per page

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

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...

Schwartz kernel theorem in algebras of generalized functions

Vincent Valmorin (2010)

Banach Center Publications

A new approach to the generalization of Schwartz’s kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of G ∞ -generalized functions class are given. A straightforward relationship between the classical and the generalized versions...

Sheaf theory and regularity. Application to local and microlocal analysis

Jean-André Marti (2010)

Banach Center Publications

A review of some methods in sheaf theory is presented to make precise a general concept of regularity in algebras or spaces of generalized functions. This leads to the local analysis of the sections of sheaves or presheaves under consideration and then to microlocal analysis and microlocal asymptotic analysis.

Tensor valued Colombeau functions on manifolds

M. Grosser (2010)

Banach Center Publications

Extending the construction of the algebra ^ ( M ) of scalar valued Colombeau functions on a smooth manifold M (cf. [4]), we present a suitable basic space for eventually obtaining tensor valued generalized functions on M, via the usual quotient construction. This basic space canonically contains the tensor valued distributions and permits a natural extension of the classical Lie derivative. Its members are smooth functions depending-via a third slot-on so-called transport operators, in addition to slots...

Currently displaying 41 – 53 of 53

Previous Page 3