Rapidly converging approximations and regularity theory

2009/06/07 by Shantanu Dave, Dave, Shantanu
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA

paper · pdf · doi:10.48550/arxiv.0906.1374

23 Pages

arxiv created 2009/06/07 · arxiv updated 2009/12/01

Abstract

We consider distributions on a closed compact manifold M as maps on smoothing operators. Thus spaces of certain maps between Ψ^-∞(M)→ C^∞(M) are considered as generalized functions. For any collection of regularizing processes we produce an algebra of generalized functions and a diffeomorphism equivariant embedding of distributions into this algebra. We provide examples invariant under certain group actions. The regularity for such generalized functions is provided in terms of a certain tameness of maps between graded Frechét spaces. This notion of regularity implies the regularity in Colombeau algebras in the \maG^∞ sense.

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