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Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$
 
Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$
eBook ISBN:  978-1-4704-0114-6
Product Code:  MEMO/111/535.E
List Price: $44.00
MAA Member Price: $39.60
AMS Member Price: $26.40
Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$
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Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$
eBook ISBN:  978-1-4704-0114-6
Product Code:  MEMO/111/535.E
List Price: $44.00
MAA Member Price: $39.60
AMS Member Price: $26.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1111994; 146 pp
    MSC: Primary 42; 41

    Bounds for orthogonal polynomials which hold on the whole interval of orthogonality are crucial to investigating mean convergence of orthogonal expansions, weighted approximation theory, and the structure of weighted spaces. This book focuses on a method of obtaining such bounds for orthogonal polynomials (and their Christoffel functions) associated with weights on \([-1,1]\). Levin and Lubinsky obtain such bounds for weights that vanish strongly at 1 and \(-1\). They also present uniform estimates of spacing of zeros of orthogonal polynomials and applications to weighted approximation theory.

    Readership

    Mathematicians interested in orthogonal polynomials, harmonic analysis, approximation theory, special functions, and potential theory.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction and results
    • 2. Some ideas behind the proofs
    • 3. Technical estimates
    • 4. Estimates for the density functions $\mu _n$
    • 5. Majorization functions and integral equations
    • 6. The proof of Theorem 1.7
    • 7. Lower bounds for $\lambda _n$
    • 8. Discretisation of a potential: Theorem 1.6
    • 9. Upper bounds for $\lambda _n$: Theorems 1.2 and Corollary 1.3
    • 10. Zeros: Corollary 1.4
    • 11. Bounds on orthogonal polynomials: Corollary 1.5
    • 12. $L_p$ Norms of orthonormal polynomials: Theorem 1.8
  • Reviews
     
     
    • Contains important ideas ... essential to anyone interested in the analysis of orthogonal polynomials.

      Journal of Approximation Theory
  • 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
Volume: 1111994; 146 pp
MSC: Primary 42; 41

Bounds for orthogonal polynomials which hold on the whole interval of orthogonality are crucial to investigating mean convergence of orthogonal expansions, weighted approximation theory, and the structure of weighted spaces. This book focuses on a method of obtaining such bounds for orthogonal polynomials (and their Christoffel functions) associated with weights on \([-1,1]\). Levin and Lubinsky obtain such bounds for weights that vanish strongly at 1 and \(-1\). They also present uniform estimates of spacing of zeros of orthogonal polynomials and applications to weighted approximation theory.

Readership

Mathematicians interested in orthogonal polynomials, harmonic analysis, approximation theory, special functions, and potential theory.

  • Chapters
  • 1. Introduction and results
  • 2. Some ideas behind the proofs
  • 3. Technical estimates
  • 4. Estimates for the density functions $\mu _n$
  • 5. Majorization functions and integral equations
  • 6. The proof of Theorem 1.7
  • 7. Lower bounds for $\lambda _n$
  • 8. Discretisation of a potential: Theorem 1.6
  • 9. Upper bounds for $\lambda _n$: Theorems 1.2 and Corollary 1.3
  • 10. Zeros: Corollary 1.4
  • 11. Bounds on orthogonal polynomials: Corollary 1.5
  • 12. $L_p$ Norms of orthonormal polynomials: Theorem 1.8
  • Contains important ideas ... essential to anyone interested in the analysis of orthogonal polynomials.

    Journal of Approximation Theory
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
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