A degree theory for compact perturbations of proper Fredholm mappings of index 0.
We present a geometric approach to diffeomorphism invariant full Colombeau algebras which allows a particularly clear view of the construction of the intrinsically defined algebra on the manifold M given in [gksv].
This paper deals with homeomorphisms F: X → Y, between Banach spaces X and Y, which are of the form where is a continuous (2n+1)-linear operator.
We prove a uniform version of the converse Taylor theorem in infinite-dimensional spaces with an explicit relation between the moduli of continuity for mappings on a general open domain. We show that if the domain is convex and bounded, then we can extend the estimate up to the boundary.
We show that a -smooth mapping on an open subset of , , can be approximated in a fine topology and together with its derivatives by a restriction of a holomorphic mapping with explicitly described domain. As a corollary we obtain a generalisation of the Carleman-Scheinberg theorem on approximation by entire functions.