Walsh Equiconvergence of Complex Interpolating Polynomials

1) but not inz? ?, then the di?erence between the Lagrange interpolant to it th in the n roots of unity and the partial sums of degree n? 1 of the Taylor 2 series about the origin, tends to zero in a larger disc of radius ?, although both operators converge to f(z) only forz

From the reviews:

"This book, written by three leading experts in interpolation and approximation theory, is a collection of new and old results stemming from the ... theorem of Walsh (1932) ... . The book is quite accessible ... . There are 11 chapters, each ending with some historical remarks, very appropriate for a monograph of this character. ... this book is a valuable source of information about this nice topic of complex approximation theory, containing many results that so far were available only in research papers." (Andrei Martínez Finkelshtein, Zentralblatt MATH, Vol. 1093 (19), 2006)

"This elegant and interesting book treats a topic that grew out of a clever observation of Joseph Walsh, for many years one of America’s pre-eminent approximators. ... The authors of the book are prominent contributors to this topic, and so especially suited to chronicle its development. ... All in all, this is a nice book, and readers can dip into it to learn about many different topics, through the lens of equiconvergence." (D. S. Lubinsky, Mathematical Reviews, Issue 2007 b)