Tensor valued Colombeau functions on manifolds

• Autorzy: M. Grosser
• Języki publikacji: EN

Abstrakty

EN

Extending the construction of the algebra $\hat{𝒢}(M)$ 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 one (smooth n-forms on M) and two (points of M) from the scalar case.

Kategorie tematyczne

• 46F30: Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
• 53A45: Vector and tensor analysis
• 46T30: Distributions and generalized functions on nonlinear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 88
• Numer: 1
• Strony: 145-152

Daty

wydano

2010

Twórcy

autor

M. Grosser

• Faculty of Mathematics, University of Vienna, Nordbergstraße 15, A-1090 Wien, Austria

Identyfikatory

DOI

10.4064/bc88-0-11