Colloquium Publications 1935; 405 pp; softcover Volume: 20 Reprint/Revision History: reprinted 1956; seventh printing 1998 ISBN10: 0821810200 ISBN13: 9780821810200 List Price: US$75 Member Price: US$60 Order Code: COLL/20
 The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's seriesthe title "Generalizations of Taylor's Series" would be appropriate. Table of Contents  Possibility of approximation, analytic functions
 Possibility of approximation, continued
 Interpolation and lemniscates
 Degree of convergence of polynomials. Overconvergence
 Best Approximation by polynomials
 Orthogonality and least squares
 Interpolation by polynomials
 Interpolation by rational functions
 Approximation by rational functions
 Interpolation and functions analytic in the unit circle
 Approximation with auxiliary conditions and to nonanalytic functions
 Existence and uniqueness of rational functions of best approximation
 Appendix
 Bibliography
 Index
