Group invariant Colombeau generalized functions |
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Authors: | Hans Vernaeve |
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Institution: | (1) University of Innsbruck, Innsbruck, Austria |
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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.
Supported by research grants M949 and Y237 of the Austrian Science Foundation (FWF).
Author’s address: Institut für Grundlagen der Bauingenieurwissenschaften, Technikerstra?e 13, 6020 Innsbruck, Austria |
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Keywords: | 2000 Mathematics Subject Classification: 46F30 35D05 |
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