This book presents a systematic and in-depth treatment of some basic topics in approximation theory in an effort to emphasize the rich connections of different branches of analysis with this subject. It contains a good blend of both the classical as well as abstract topics in the domain and their interconnections as appropriate. The approach is from the very concrete to more and more abstract levels. In order to provide a historical perspective on the results, a section on notes is appended to each chapter with an extensive bibliography. Researchers will find several references to recent developments. Problems of varying degree of difficulty accompany each chapter. Some of these problems complement certain results from the text. The others, more challenging, are drawn from the contemporary research articles. Ample hints are provided for such problems. Primarily aimed at graduate students and teachers of mathematics, researchers interested in an introduction to the specific results or techniques of approximation theory will find this book very attractive.
What reviewers said about the First Edition: "there are a few novel features in the book such as the use of the Peetre K-functional, the topic of Hermite-Birkhoff interpolation, and the use of complex variable methods in the study of Fourier series". "A graduate student who was fluent in this book would be prepared for research in almost any area of approximation theory". (F. Deutsch in "Mathematical Reviews", AMS). "This is a rich book and a valuable addition to the literature in a fast growing field". (D. Gaier in "Zentralblatt fur Mathematik"). "I think the book will become a standard reference in the field". (S.Cobzas in Studia Univ. "Babes-Bolyai", Mathematica).
H. N. Mhaskar.: Department of Computer Science California State University, Los Angeles, California, USA D. V. Pai.: Department of Mathematics Indian Institute of Technology Bombay, Mumbai
Density Theorems / Linear Chebyshev Approximation / Degree of Approximation / Interpolation / Fourier Series / Spline Functions / Orthogonal Polynomials / Best Approximation in Normed Linear Spaces / Bibliography / Symbols and Notation / Index.