**Memoirs of the American Mathematical Society**

2008;
161 pp;
Softcover

MSC: Primary 30; 41;
Secondary 31

Print ISBN: 978-0-8218-4063-4

Product Code: MEMO/192/897

List Price: $75.00

AMS Member Price: $45.00

MAA Member Price: $67.50

**Electronic ISBN: 978-1-4704-0503-8
Product Code: MEMO/192/897.E**

List Price: $75.00

AMS Member Price: $45.00

MAA Member Price: $67.50

# Limit Theorems of Polynomial Approximation with Exponential Weights

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*Michael I. Ganzburg*

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

# Table of Contents

## Limit Theorems of Polynomial Approximation with Exponential Weights

- Contents v6 free
- Chapter 1. Introduction 110 free
- Chapter 2. Statement of Main Results 1524
- Chapter 3. Properties of Harmonic Functions 1928
- Chapter 4. Polynomial Inequalities with Exponential Weights 4352
- Chapter 5. Entire Functions of Exponential Type and their Approximation Properties 5968
- Chapter 6. Polynomial Interpolation and Approximation of Entire Functions of Exponential Type 6776
- Chapter 7. Proofs of the Limit Theorems 7786
- Chapter 8. Applications 8594
- Chapter 9. Multidimensional Limit Theorems of Polynomial Approximation with Exponential Weights 105114
- Chapter 10. Examples 117126
- Appendix A. Appendix. Negativity of a Kernel 137146
- Bibliography 155164
- Index 161170 free