Polynomial Approximation Theory

Abstract

In the remainder of this book we concentrate on summarizing the fundamental spectral methods theory for approximation errors, stability and convergence, and apply this to the analysis of model equations. We will not present here all the details of all the proofs of the results that are cited. Rather, we illustrate the basic principles of the theory by presenting proofs for representative results. In many cases these proofs are delayed until later in the chapter (in the interests of having a coherent summary). For the same reason bibliographic references for the main contributions to the theory are likewise deferred to the end of the appropriate section.

An erratum to this chapter is available at http://dx.doi.org/10.1007/978-3-540-30726-6_8 .