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Group invariant Colombeau generalized functions

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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.

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Authors and Affiliations

  1. University of Innsbruck, Innsbruck, Austria

    Hans Vernaeve

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  1. Hans Vernaeve
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Correspondence to Hans Vernaeve.

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Supported by research grants M949 and Y237 of the Austrian Science Foundation (FWF).

Author’s address: Institut für Grundlagen der Bauingenieurwissenschaften, Technikerstraße 13, 6020 Innsbruck, Austria

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Vernaeve, H. Group invariant Colombeau generalized functions. Monatsh Math 153, 165–175 (2008). https://doi.org/10.1007/s00605-007-0485-1

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  • DOI: https://doi.org/10.1007/s00605-007-0485-1

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