eBook ISBN:  9781470405038 
Product Code:  MEMO/192/897.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $45.00 
eBook ISBN:  9781470405038 
Product Code:  MEMO/192/897.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $45.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 192; 2008; 161 ppMSC: Primary 30; 41; Secondary 31
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

Chapters

1. Introduction

2. Statement of main results

3. Properties of harmonic functions

4. Polynomial inequalities with exponential weights

5. Entire functions of exponential type and their approximation properties

6. Polynomial interpolation and approximation of entire functions of exponential type

7. Proofs of the limit theorems

8. Applications

9. Multidimensional limit theorems of polynomial approximation with exponential weights

10. Examples


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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.

Chapters

1. Introduction

2. Statement of main results

3. Properties of harmonic functions

4. Polynomial inequalities with exponential weights

5. Entire functions of exponential type and their approximation properties

6. Polynomial interpolation and approximation of entire functions of exponential type

7. Proofs of the limit theorems

8. Applications

9. Multidimensional limit theorems of polynomial approximation with exponential weights

10. Examples