Strongly internal sets and generalized smooth functions (Q458302)
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scientific article; zbMATH DE number 6351981
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Strongly internal sets and generalized smooth functions |
scientific article; zbMATH DE number 6351981 |
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Strongly internal sets and generalized smooth functions (English)
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7 October 2014
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Colombeau generalized functions
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strongly internal sets
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generalized smooth functions
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The authors introduce a generalization of Colombeau-type generalized functions, which they call generalized smooth functions,NEWLINEGSF. These functions are set-theoretic maps on sets of generalized points that satisfy the minimal logical conditions necessary to obtain well-defined maps obeying the standard asymptotic estimates of the Colombeau approach. They are the natural extension of Colombeau generalized functions to general domains and they display optimal set-theoretical properties. The authors give proofs that GSF functions are locally Lipschitz functions. Also, this notion is studied for functions defined on and valued in generalized points.
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