Screen LibraryDiscrete orthogonal polynomials. (am-164): asymptotics and applications (am-164) : asymptotics and applications (am-164) /
This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case...
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| Main Authors: | |
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| Corporate Authors: | |
| Group Author: | ; ; |
| Published: |
Princeton University Press,
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| Publisher Address: | Princeton, N.J. : |
| Publication Dates: |
[2007] ©2007 |
| Literature type: | eBook |
| Language: | English |
| Edition: | Course Book. |
| Series: |
Annals of mathematics studies;
164 |
| Subjects: | |
| Online Access: |
http://dx.doi.org/10.1515/9781400837137 http://www.degruyter.com/doc/cover/9781400837137.jpg |
| Summary: |
This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case. J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis. |
| Carrier Form: | 1 online resource (184 pages) : illustrations. |
| ISBN: | 9781400837137 |
| Index Number: | QA404 |
| CLC: | O174.21 |
| Contents: |
Frontmatter -- Contents -- Preface -- Chapter 1. Introduction -- Chapter 2. Asymptotics of General Discrete Orthogonal Polynomials in the Complex Plane -- Chapter 3. Applications -- Chapter 4. An Equivalent Riemann-Hilbert Problem -- Chapter 5. Asymptotic Analysis -- Chapter 6. Discrete Orthogonal Polynomials: Proofs of Theorems Stated in 2.3 -- Chapter 7. Universality: Proofs of Theorems Stated in 3.3 -- Appendix A. The Explicit Solution of Riemann-Hilbert Problem 5.1 -- Appendix B. Construction of the Hahn Equilibrium Measure: the Proof of Theorem 2.17 -- Appendix C. List of Important Symbols -- Bibliography -- Index. |