Ge´za Freud, orthogonal polynomials and Christoffel functions. A case study

I. Foreword 2. The thesis 3. Notations 4. Justification of the claim 4.1. A little philosophy Part 1: Orthogonal polynomials on /inite intervals and on the untt crrcle 4.2. One-sided approximations and Tauberian theorems with remainder terms 4.3. Convergence and absolute convergence of orthogonal Fourier series and Lebesgue functions 4.4. Strong Cesaro summability of orthogonal Fourier series 4.5. Asymptotics for Christoffel functions 4.6. How Grenander and Rosenblatt and Geronimus erred 4.7. Quadrature sums and Christoffel functions 4.8. Mean convergence of Lagrange interpolation 4.9. Zeros of orthogonal polynomials and eigenvalues of Toeplitz matrices 4.10. Hermite-Fejer interpolation and derivatives of Christoffel functions 4.1 I Szegii’s theory via Christoffel functions 4.12. Asymptotics for orthogonal polynomials and equiconvergence of orthogonal Fourier series 4.13. Stepping beyond Szegb’s theory 4.14. Farewell to orthogonal polynomials in finite intervals Part 2: Orthogonal pol,vnomials on infinite internals 4.15. Freud weights 4.16. Christoffcl functions for Freud weights 4.17. Orthogonal Fourier series, Cesaro and de la VallteePoussin means, and BernsteinMarkov and Nikolskri inequalities with Freud weights 4.18. Freud conjectures 4.19. Quadrature sums and Lagrange interpolation revisited 4.20. Differential equations and Freud polynomials 4.21. Plancherel-Rotach asymptotics for orthogonal polynomials with Freud weights 4.22. Plancherel-Rotach asymptotics for Christoffel functions with Freud weights 5. Epilogue Acknowledgments References