Asymptotic scales-asymptotic algebras

Abstract

Abstract J.F. Colombeau and other authors have introduced algebras of generalized functions in order to solve differential problems which have no solution in spaces of distributions. These algebras are based on properties of polynomial growth with respect to a parameter. We generalize here this construction to every asymptotic scale and give examples of such generalized algebras and apply the theory to differential problems. Keywords: asymptotic scaleasymptotic algebrageneralized functionsMSC(1991): 26E9934E1035D9946F99