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Monatshefte für Mathematik

, Volume 153, Issue 2, pp 165–175 | Cite as

Group invariant Colombeau generalized functions

  • Hans Vernaeve
Article

Abstract.

Colombeau generalized functions invariant under smooth (additive) one-parameter groups are characterized. This characterization is applied to generalized functions invariant under orthogonal groups of arbitrary signature, such as groups of rotations or the Lorentz group. Further, a one-dimensional Colombeau generalized function with two (real) periods is shown to be a generalized constant, when the ratio of the periods is an algebraic nonrational number. Finally, a nonstandard Colombeau generalized function invariant under standard translations is shown to be constant.

2000 Mathematics Subject Classification: 46F30, 35D05 
Key words: Colombeau generalized functions, translation invariance, rotational invariance, Lorentz invariance, generalized one-parameter groups 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.University of InnsbruckInnsbruckAustria

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