661 Modern Trends in Constructive Function Theory Constructive Functions 2014 Conference in Honor of Ed Saff’s 70th Birthday May 26–30, 2014 Vanderbilt University, Nashville, Tennessee Douglas P. Hardin Doron S. Lubinsky Brian Z. Simanek Editors AmericanMathematicalSociety Licensed to AMS. License or copyright restrictions may apply to redistribution; see http://www.ams.org/publications/ebooks/terms Modern Trends in Constructive Function Theory Constructive Functions 2014 Conference in Honor of Ed Saff’s 70th Birthday May 26–30, 2014 Vanderbilt University, Nashville, Tennessee Douglas P. Hardin Doron S. Lubinsky Brian Z. Simanek Editors Licensed to AMS. License or copyright restrictions may apply to redistribution; see http://www.ams.org/publications/ebooks/terms Licensed to AMS. License or copyright restrictions may apply to redistribution; see http://www.ams.org/publications/ebooks/terms 661 Modern Trends in Constructive Function Theory Constructive Functions 2014 Conference in Honor of Ed Saff’s 70th Birthday May 26–30, 2014 Vanderbilt University, Nashville, Tennessee Douglas P. Hardin Doron S. Lubinsky Brian Z. Simanek Editors AmericanMathematicalSociety Providence,RhodeIsland Licensed to AMS. License or copyright restrictions may apply to redistribution; see http://www.ams.org/publications/ebooks/terms EDITORIAL COMMITTEE Dennis DeTurck, Managing Editor Michael Loss Kailash Misra Catherine Yan 2010 Mathematics Subject Classification. Primary 11P21,26C10, 31A15, 33C50, 35L67, 40A15, 41A21, 42C05, 60B20. Library of Congress Cataloging-in-Publication Data Modern trends in constructive function theory : conference in honor of Ed Saff’s 70th birthday : constructive functions 2014, May 26-30, 2014, Vanderbilt University, Nashville, Ten- nessee/DouglasP.Hardin,DoronS.Lubinsky,BrianZ.Simanek,editors. pagescm. –(Contemporarymathematics;volume661) Includesbibliographicalreferences. ISBN978-1-4704-2534-0(alk. paper) 1. Functions–Congresses. 2. Approximation theory–Congresses. 3. Mathematical analysis– Congresses. I. Saff, E. B., 1944– II. Hardin, Douglas Patten, 1958– editor. III. Lubinsky, D.S.(DoronShaul),1955–editor. IV.Simanek,BrianZ.,1985–editor. QA331.M6772016 511.3’26–dc23 2015035790 ContemporaryMathematicsISSN:0271-4132(print);ISSN:1098-3627(online) DOI:http://dx.doi.org/10.1090/conm/661 Color graphic policy. Any graphics created in color will be rendered in grayscale for the printedversionunlesscolorprintingisauthorizedbythePublisher. 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License or copyright restrictions may apply to redistribution; see http://www.ams.org/publications/ebooks/terms Licensed to AMS. License or copyright restrictions may apply to redistribution; see http://www.ams.org/publications/ebooks/terms Contents Preface ix Ed Saff at Three Score and Ten Doron S. Lubinsky 1 The Tale of a Formula Vilmos Totik 29 Log-optimal Configurations on the Sphere P. D. Dragnev 41 Convergence of Random Continued Fractions and Random Iterations of M¨obius Transformations Lisa Lorentzen 57 Ratio Asymptotics for Multiple Orthogonal Polynomials Walter Van Assche 73 Study of a Parameterization of the Bivariate Trigonometric Moment Problem Jeffrey S. Geronimo and Andrew Pangia 87 Explicit Formulas for the Riesz Energy of the Nth Roots of Unity J. S. Brauchart 101 Asymptotic Zero Distribution of Random Polynomials Spanned by General Bases Igor E. Pritsker 121 On Row Sequences of Pad´e and Hermite-Pad´e Approximation G. Lo´pez-Lagomasino 141 Orthogonal Expansions for Generalized Gegenbauer Weight Function on the Unit Ball Yuan Xu 153 The Mhaskar–Saff Variational Principle and Location of the Shocks of Certain Hyperbolic Equations A. I. Aptekarev 167 vii Licensed to AMS. License or copyright restrictions may apply to redistribution; see http://www.ams.org/publications/ebooks/terms viii CONTENTS Boundary Estimates for Bergman Polynomials in Domains with Corners N. Stylianopoulos 187 Asymptotics of Type I Hermite–Pad´e Polynomials for Semiclassical Functions Andrei Mart´ınez-Finkelshtein, Evguenii Rakhmanov, and Sergey P. Suetin 199 Sparse Interpolation and Rational Approximation Annie Cuyt and Wen-shin Lee 229 Asymptotics of the Meijer G-functions Yu Lin and R. Wong 243 Transformations of Polynomial Ensembles Arno B. J. Kuijlaars 253 Local Statistics of Lattice Points on the Sphere Jean Bourgain, Peter Sarnak, and Ze´ev Rudnick 269 Conditioning Moments of Singular Measures for Entropy Maximization II: Numerical Examples Marko Budi˘sic´ and Mihai Putinar 283 Licensed to AMS. License or copyright restrictions may apply to redistribution; see http://www.ams.org/publications/ebooks/terms Preface This volume contains papers submitted by colleagues of Ed Saff and distin- guished participants in the Constructive Functions 2014 Conference and School held from May 26 to May 30 at Vanderbilt University in Nashville, TN, USA. The conference and this volume are dedicated to Ed Saff on the occasion of his 70th birthday and aim to celebrate the influential role Ed has played in the fields of constructive function theory, approximation theory, potential theory, and applied mathematics. Many of these papers reflect the content of the talk one or more of the authors presented at the conference. The wide breadth of the subject areas discussedinthisvolumehighlightstheextentofEdSaff’sinfluenceinmathematics over the last 40 years. It is a pleasure to dedicate this volume to him. TheConstructiveFunctions2014ConferenceandSchoolfeaturedover140par- ticipants from 30 countries. There were eleven plenary addresses complemented by more than 100 contributed talks in subjects ranging from random matrix the- oryandRiemann-Hilbert analysis tonumerical analysisandapproximation theory. Of particular note were the expository school lectures given by four prominent mathematicians and aimed at an audience of early career mathematicians. These 75-minute lectures were presented on Riemann-Hilbert analysis, numerical analy- sis and approximation, spectral theory on finite gap sets, and sphere packing and discrete minimal energy. Without the tireless efforts of many individuals, the Constructive Functions 2014 Conference and School would not have been possible. While an accurate list would be too lengthy to include here, we must single out the contributions of the National Science Foundation (grant DMS-1363146), Springer Publishing, Pearson Publishing, the Society for Industrial and Applied Mathematics (SIAM), Loretta Saff, and the mathematics department staff at Vanderbilt University. Special thanks are also due to Christine Thivierge and the technical staff of the American Mathematical Society for their efforts in creating this volume. Finally,wewouldliketothanktheparticipantsoftheConstructiveFunctions2014 Conference and School whose continuing efforts make this research field such an exciting frontier. Douglas P. Hardin Doron S. Lubinsky Brian Z. Simanek ix Licensed to AMS. License or copyright restrictions may apply to redistribution; see http://www.ams.org/publications/ebooks/terms