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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.
List of contents
Preface.- Some notes on trigonometric approximation.- The end points effect.- Looking for new moduli.- Exact estimates and asymptotic.- Construction of special operators.- Bibliography.
Summary
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.
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From the reviews:
“This book is a survey of several topics in algebraic polynomial approximation on a finite interval, mostly related to the degree of approximation. … The book can be of great help to researchers, both those taking their first steps in the subject and veteran researchers who need to check references.” (D. Leviatan, Mathematical Reviews, September, 2013)
“The monograph presents an exposition of results related to direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. … The main achievement of the book is that it gathers some different known solutions to problems in algebraic approximation that are not collected in other text books. … this book is a very helpful tool for students and researchers interested in approximation by algebraic polynomials.” (Daniel Cárdenas-Morales, Zentralblatt MATH, Vol. 1248, 2012)
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From the reviews:
"This book is a survey of several topics in algebraic polynomial approximation on a finite interval, mostly related to the degree of approximation. ... The book can be of great help to researchers, both those taking their first steps in the subject and veteran researchers who need to check references." (D. Leviatan, Mathematical Reviews, September, 2013)
"The monograph presents an exposition of results related to direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. ... The main achievement of the book is that it gathers some different known solutions to problems in algebraic approximation that are not collected in other text books. ... this book is a very helpful tool for students and researchers interested in approximation by algebraic polynomials." (Daniel Cárdenas-Morales, Zentralblatt MATH, Vol. 1248, 2012)
