Strongly internal sets and generalized smooth functions
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.
scientific article; zbMATH DE number 6351981
scientific article