Nonlinear analysis and approximation theory: Five applications to Haar manifolds

Five freestanding chapters apply basic results from Convex Analysis and Differential Geometry to problems in Approximation Theory. The generic problem occurs in a space of continuous functions and is to minimize the distance between a given function from a specified subset of continuous functions. The contents of the chapters are: (1) Demonstrating the existence of an asymptotic expansion for the Polya Algorithm; (2) Deriving an alternation theorem characterizing best complex approximations for special cases; (3) Providing sufficient conditions which assert that a manifold admits unique best approximations; (4) Using the contingent cone to characterize best approximations from several classes of rational functions; (5) Demonstrating the existence of a best approximation flow.