Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Approximation of Functions: Second Edition
 
G. G. Lorentz
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-7363-1
Product Code:  CHEL/322.S
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $30.60
eBook ISBN:  978-1-4704-7494-2
Product Code:  CHEL/322.E
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $30.60
Softcover ISBN:  978-1-4704-7363-1
eBook: ISBN:  978-1-4704-7494-2
Product Code:  CHEL/322.S.B
List Price: $68.00 $51.00
MAA Member Price: $61.20 $45.90
AMS Member Price: $61.20 $45.90
Add to cart
Click above image for expanded view
Approximation of Functions: Second Edition
G. G. Lorentz
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-7363-1
Product Code:  CHEL/322.S
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $30.60
eBook ISBN:  978-1-4704-7494-2
Product Code:  CHEL/322.E
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $30.60
Softcover ISBN:  978-1-4704-7363-1
eBook ISBN:  978-1-4704-7494-2
Product Code:  CHEL/322.S.B
List Price: $68.00 $51.00
MAA Member Price: $61.20 $45.90
AMS Member Price: $61.20 $45.90
Add to cart
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 322; 1986; 188 pp
    MSC: Primary 41

    This is an easily accessible book on the approximation of functions—simple and without unnecessary details, but complete enough to include the main results of the theory. Except for a few sections, only functions of a real variable are treated. This work can be used as a textbook for graduate or advanced undergraduate courses or for self-study. Included in the volume are Notes at the end of each chapter, Problems, and a selected Bibliography.
    Readership

    Graduate students and advanced undergraduate students interested in analysis.
  • Table of Contents
     
     
    • Front Cover
    • Preface to the Second Edition
    • Preface to the First Edition
    • Contents
    • Chapter 1. Possibility of Approximation
    • 1. Basic Notions
    • 2. Linear Operators
    • 3. Approximation Theorems
    • 4. The Theorem of Stone
    • 5. Notes
    • PROBLEMS
    • Chapter 2. Polynomials of Best Approximation
    • 1. Existence of Polynomials of Best Approximation
    • 2. Characterization of Polynomials of Best Approximation
    • 3. Applications of Convexity
    • 4. Chebyshev Systems
    • 5. Uniqueness of Polynomials of Best Approximation
    • 6. Chebyshev's Theorem
    • 7. Chebyshev Polynomials
    • 8. Approximation of Some Complex Functions
    • 9. Notes
    • PROBLEMS
    • Chapter 3. Properties of Polynomials and Moduli of Continuity
    • 1. Interpolation
    • 2. Inequalities of Bernstein
    • 3. The Inequality of Markov
    • 4. Growth of Polynomials in the Complex Plane
    • 5. Moduli of Continuity
    • 6. Moduli of Smoothness
    • 7. Classes of Functions
    • 8. Notes
    • PROBLEMS
    • Chapter 4. The Degree of Approximation by Trigonometric Polynomials
    • 1. Generalities
    • 2. The Theorem of Jackson
    • 3. The Degree of Approximation of Differentiable Functions
    • 4. Inverse Theorems
    • 5. Differentiable Functions
    • 6. Notes
    • PROBLEMS
    • Chapter 5. The Degree of Approximation by Algebraic Polynomials
    • 1. Preliminaries
    • 2. The Approximation Theorems
    • 3. Inequalities for the Derivatives of Polynomials
    • 4. Inverse Theorems
    • 5. Approximation of Analytic Functions
    • 6. Notes
    • PROBLEMS
    • Chapter 6. Approximation by Rational Functions. Functions of Several Variables
    • 1. Degree of Rational Approximation
    • 2. Further Theorems
    • 3. Periodic Functions of Several Variables
    • 4. Approximation by Algebraic Polynomials
    • 5. Notes
    • PROBLEMS
    • Chapter 7. Approximation by Linear Polynomial Operators
    • 1. Sums of de la Vallee-Poussin. Positive Operators
    • 2. The Principle of Uniform Boundedness
    • 3. Operators that Preserve Trigonometric Polynomials
    • 4. Trigonometric Saturation Classes
    • 5. The Saturation Class of the Bernstein Polynomials
    • 6. Notes
    • PROBLEMS
    • Chapter 8. Approximation of Classes of Functions
    • 1. Introduction
    • 2. Approximation in the Space L1
    • 3. The Degree of Approximation of the Classes W*p
    • 4. Distance Matrices
    • 5. Approximation of the Classes Λω
    • 6. Arbitrary Moduli of Continuity; Approximation by Operators
    • 7. Analytic Functions
    • 8. Notes
    • PROBLEMS
    • Chapter 9. Widths
    • 1. Definitions and Basic Properties
    • 2. Sets of Continuous and Differentiable Functions
    • 3. Widths of Balls
    • 4. Applications of Theorem 2
    • 5. Differential Operators
    • 6. Widths of the Set R1
    • 7. Notes
    • PROBLEMS
    • Chapter 10. Entropy
    • 1. Entropy and Capacity
    • 2. Sets of Continuous and Differentiable Functions
    • 3. Entropy of Classes of Analytic Functions
    • 4. General Sets of Analytic Functions
    • 5. Relations between Entropy and Widths
    • 6. Notes
    • PROBLEMS
    • Chapter 11. Representation of Functions of Several Variables by Functions of One Variable
    • 1. The Theorem of Kolmogorov
    • 2. The Fundamental Lemma
    • 3. The Completion of the Proof
    • 4. Functions Not Representable by Superpositions
    • 5. Notes
    • PROBLEMS
    • Bibliography
    • Index
    • Back Cover
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
AMS Chelsea Publishing
Volume: 322; 1986; 188 pp
MSC: Primary 41

This is an easily accessible book on the approximation of functions—simple and without unnecessary details, but complete enough to include the main results of the theory. Except for a few sections, only functions of a real variable are treated. This work can be used as a textbook for graduate or advanced undergraduate courses or for self-study. Included in the volume are Notes at the end of each chapter, Problems, and a selected Bibliography.
Readership

Graduate students and advanced undergraduate students interested in analysis.
  • Front Cover
  • Preface to the Second Edition
  • Preface to the First Edition
  • Contents
  • Chapter 1. Possibility of Approximation
  • 1. Basic Notions
  • 2. Linear Operators
  • 3. Approximation Theorems
  • 4. The Theorem of Stone
  • 5. Notes
  • PROBLEMS
  • Chapter 2. Polynomials of Best Approximation
  • 1. Existence of Polynomials of Best Approximation
  • 2. Characterization of Polynomials of Best Approximation
  • 3. Applications of Convexity
  • 4. Chebyshev Systems
  • 5. Uniqueness of Polynomials of Best Approximation
  • 6. Chebyshev's Theorem
  • 7. Chebyshev Polynomials
  • 8. Approximation of Some Complex Functions
  • 9. Notes
  • PROBLEMS
  • Chapter 3. Properties of Polynomials and Moduli of Continuity
  • 1. Interpolation
  • 2. Inequalities of Bernstein
  • 3. The Inequality of Markov
  • 4. Growth of Polynomials in the Complex Plane
  • 5. Moduli of Continuity
  • 6. Moduli of Smoothness
  • 7. Classes of Functions
  • 8. Notes
  • PROBLEMS
  • Chapter 4. The Degree of Approximation by Trigonometric Polynomials
  • 1. Generalities
  • 2. The Theorem of Jackson
  • 3. The Degree of Approximation of Differentiable Functions
  • 4. Inverse Theorems
  • 5. Differentiable Functions
  • 6. Notes
  • PROBLEMS
  • Chapter 5. The Degree of Approximation by Algebraic Polynomials
  • 1. Preliminaries
  • 2. The Approximation Theorems
  • 3. Inequalities for the Derivatives of Polynomials
  • 4. Inverse Theorems
  • 5. Approximation of Analytic Functions
  • 6. Notes
  • PROBLEMS
  • Chapter 6. Approximation by Rational Functions. Functions of Several Variables
  • 1. Degree of Rational Approximation
  • 2. Further Theorems
  • 3. Periodic Functions of Several Variables
  • 4. Approximation by Algebraic Polynomials
  • 5. Notes
  • PROBLEMS
  • Chapter 7. Approximation by Linear Polynomial Operators
  • 1. Sums of de la Vallee-Poussin. Positive Operators
  • 2. The Principle of Uniform Boundedness
  • 3. Operators that Preserve Trigonometric Polynomials
  • 4. Trigonometric Saturation Classes
  • 5. The Saturation Class of the Bernstein Polynomials
  • 6. Notes
  • PROBLEMS
  • Chapter 8. Approximation of Classes of Functions
  • 1. Introduction
  • 2. Approximation in the Space L1
  • 3. The Degree of Approximation of the Classes W*p
  • 4. Distance Matrices
  • 5. Approximation of the Classes Λω
  • 6. Arbitrary Moduli of Continuity; Approximation by Operators
  • 7. Analytic Functions
  • 8. Notes
  • PROBLEMS
  • Chapter 9. Widths
  • 1. Definitions and Basic Properties
  • 2. Sets of Continuous and Differentiable Functions
  • 3. Widths of Balls
  • 4. Applications of Theorem 2
  • 5. Differential Operators
  • 6. Widths of the Set R1
  • 7. Notes
  • PROBLEMS
  • Chapter 10. Entropy
  • 1. Entropy and Capacity
  • 2. Sets of Continuous and Differentiable Functions
  • 3. Entropy of Classes of Analytic Functions
  • 4. General Sets of Analytic Functions
  • 5. Relations between Entropy and Widths
  • 6. Notes
  • PROBLEMS
  • Chapter 11. Representation of Functions of Several Variables by Functions of One Variable
  • 1. The Theorem of Kolmogorov
  • 2. The Fundamental Lemma
  • 3. The Completion of the Proof
  • 4. Functions Not Representable by Superpositions
  • 5. Notes
  • PROBLEMS
  • Bibliography
  • Index
  • Back Cover
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Powered by MathJax
Please select which format for which you are requesting permissions.