RATIONAL APPROXIMATION AND EXOTIC LIPSCHITZ SPACES

Publisher Summary This chapter provides an overview of the rational approximation and exotic Lipschitz spaces. It also discusses the relationship between the structural properties of a function and its degree of approximation by rational functions. The chapter presents a scenario in which the function f is in R α p and where it can be changed on a. set of arbitrarily small measure so that the resulting function F has continuous derivatives of order less than α. If one stays in the scaleofLipschitzspacesthenno further improvement of the resultispossible.The combination of methods of rational approximation and of the local polynomial approximation plays an important part to prove the main theorem.