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Christoffel functions and orthogonal polynomials for exponential weights on $[-1,1]$

About this Title

A. L. Levin and D. S. Lubinsky

Publication: Memoirs of the American Mathematical Society
Publication Year 1994: Volume 111, Number 535
ISBNs: 978-0-8218-2599-0 (print); 978-1-4704-0114-6 (online)
MathSciNet review: 1222183
MSC: Primary 41-02; Secondary 41A10, 41A17, 41A25, 42C05

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Table of Contents


  • 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