Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications
About this Title
J. Arvesú, Universidad Carlos III de Madrid, Leganés, Spain and G. López Lagomasino, Universidad Carlos III de Madrid, Leganés, Spain, Editors
Publication: Contemporary Mathematics
Publication Year 2012: Volume 578
ISBNs: 978-0-8218-6896-6 (print); 978-0-8218-9102-5 (online)
This volume contains the proceedings of the 11th International Symposium on Orthogonal Polynomials, Special Functions, and their Applications, held August 29–September 2, 2011, at the Universidad Carlos III de Madrid in Leganés, Spain.
The papers cover asymptotic properties of polynomials on curves of the complex plane, universality behavior of sequences of orthogonal polynomials for large classes of measures and its application in random matrix theory, the Riemann–Hilbert approach in the study of Padé approximation and asymptotics of orthogonal polynomials, quantum walks and CMV matrices, spectral modifications of linear functionals and their effect on the associated orthogonal polynomials, bivariate orthogonal polynomials, and optimal Riesz and logarithmic energy distribution of points. The methods used include potential theory, boundary values of analytic functions, Riemann–Hilbert analysis, and the steepest descent method.
Graduate students and research mathematicians interested in special functions and orthogonal polynomials.
Table of Contents
- Manuel Alfaro and Walter Van Assche – Life and work (so far) of Paco Marcellán
- A. I. Aptekarev, J. S. Dehesa, P. Sánchez-Moreno and D. N. Tulyakov – Asymptotics of $L_p$-norms of Hermite polynomials and Rényi entropy of Rydberg oscillator states
- J. S. Brauchart, D. P. Hardin and E. B. Saff – The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere
- M. J. Cantero, L. Moral and L. Velázquez – Spectral transformations of hermitian linear functionals
- T. Claeys and S. Olver – Numerical study of higher order analogues of the Tracy–Widom distribution
- Alexandre Eremenko and Peter Yuditskii – Comb functions
- Jeffrey S. Geronimo, Plamen Iliev and Greg Knese – Orthogonality relations for bivariate Bernstein-Szegő measures
- F. Alberto Grünbaum – Quantum walks and CMV matrices
- D. S. Lubinsky – Discrete beta ensembles based on Gauss type quadratures
- Andrei Martínez-Finkelshtein, Evgenii A. Rakhmanov and Sergey P. Suetin – Heine, Hilbert, Padé, Riemann, and Stieltjes: John Nuttall’s work 25 years later
- E. A. Rakhmanov – Orthogonal Polynomials and $S$-curves
- Vilmos Totik – Fast decreasing and orthogonal polynomials