On the foundations of nonlinear generalized functions II
نویسنده
چکیده
This paper gives a comprehensive analysis of algebras of Colombeau-type generalized functions in the range between the diffeomorphism-invariant quotient algebra G = EM/N introduced in part I and Colombeau’s original algebra G . Three main results are established: First, a simple criterion describing membership in N (applicable to all types of Colombeau algebras) is given. Second, two counterexamples demonstrate that G is not injectively included in G. Finally, it is shown that in the range “between” G and G only one more construction leads to a diffeomorphism invariant algebra. In analyzing the latter, several classification results essential for obtaining an intrinsic description of G on manifolds are derived. 2000Mathematics Subject Classification. Primary 46F30; Secondary 26E15, 46E50, 35D05.
منابع مشابه
Institute for Mathematical Physics on the Foundations of Nonlinear Generalized Functions Ii
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