Memoirs of the American Mathematical Society 2008; 161 pp; softcover Volume: 192 ISBN10: 0821840630 ISBN13: 9780821840634 List Price: US$71 Individual Members: US$42.60 Institutional Members: US$56.80 Order Code: MEMO/192/897
 The author develops the limit relations between the errors of polynomial approximation in weighted metrics and apply them to various problems in approximation theory such as asymptotically best constants, convergence of polynomials, approximation of individual functions, and multidimensional limit theorems of polynomial approximation. In addition he establishes new inequalities for polynomials in complex domains and new asymptotics and estimates for orthogonal polynomials with exponential weights. More detailed information on approximation properties of functions is obtained for the canonical weights \(W(x)=\exp(x^\alpha),\, 0<\alpha<\infty\), and some other weights. Table of Contents  Introduction
 Statement of main results
 Properties of harmonic functions
 Polynomial inequalities with exponential weights
 Entire functions of exponential type and their approximation properties
 Polynomial interpolation and approximation of entire functions of exponential type
 Proofs of the limit theorems
 Applications
 Multidimensional limit theorems of polynomial approximation with exponential weights
 Examples
 Appendix A. Negativity of a kernel
 Bibliography
 Index
