This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. In addition, some facts concerning trigonometric approximation that are necessary for motivation and comparisons are included. The selection of papers that are referenced and discussed document some trends in polynomial approximation from the 1950s to the present day.

Puts together different known solutions to problems in algebraic approximation not collected in any other text book Helps finding the correct references for a specific result Comprehensive bibliographic references give a unique understanding of the evolution of approximation theory Includes supplementary material: sn.pub/extras

Klappentext

This book presents a unique survey of solutions in algebraic approximation. Several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval are discussed. Some of these results are not collected in any other book. In addition, facts concerning trigonometric approximation that are necessary for motivation and comparisons are included. The selection of papers that are referenced and discussed document trends in polynomial approximation from the 1950s to the present day.

Algebraic Approximation: A Guide to Past and Current Solutions will be invaluable to anyone seeking to understand the evolution of ideas in algebraic approximation. Its extensive bibliographic character will help finding the correct references for a specific result.

Inhalt

Preface.- Some notes on trigonometric approximation.- The end points effect.- Looking for new moduli.- Exact estimates and asymptotic.- Construction of special operators.- Bibliography.