Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorLevin, Eli. author
TitleOrthogonal Polynomials for Exponential Weights [electronic resource] / by Eli Levin, Doron S. Lubinsky
ImprintNew York, NY : Springer New York : Imprint: Springer, 2001
Connect tohttp://dx.doi.org/10.1007/978-1-4613-0201-8
Descript XI, 476 p. online resource

SUMMARY

The analysis of orthogonal polynomials associated with general weights was a major theme in classical analysis in the twentieth century, and undoubtedly will continue to grow in importance in the future. In this monograph, the authors investigate orthogonal polynomials for exponential weights defined on a finite or infinite interval. The interval should contain 0, but need not be symmetric about 0; likewise the weight need not be even. The authors establish bounds and asymptotics for orthonormal and extremal polynomials, and their associated Christoffel functions. They deduce bounds on zeros of extremal and orthogonal polynomials, and also establish Markov- Bernstein and Nikolskii inequalities. The authors have collaborated actively since 1982 on various topics, and have published many joint papers, as well as a Memoir of the American Mathematical Society. The latter deals with a special case of the weights treated in this book. In many ways, this book is the culmination of 18 years of joint work on orthogonal polynomials, drawing inspiration from the works of many researchers in the very active field of orthogonal polynomials


CONTENT

1 Introduction and Results -- 2 Weighted Potential Theory: The Basics -- 3 Basic Estimates for Q, at -- 4 Restricted Range Inequalities -- 5 Estimates for Measure and Potential -- 6 Smoothness of ?t -- 7 Weighted Polynomial Approximation -- 8 Asymptotics of Extremal Errors -- 9 Christoffel Functions -- 10 Markov-Bernstein and Nikolskii Inequalities -- 11 Zeros of Orthogonal Polynomials -- 12 Bounds on Orthogonal Polynomials -- 13 Further Bounds and Applications -- 14 Asymptotics of Extremal Polynomials -- 15 Asymptotics of Orthonormal Polynomials -- B Bernstein-Szegรถ Orthogonal Polynomials -- Notes -- References -- List of Symbols


Mathematics Topological groups Lie groups Combinatorics Mathematics Topological Groups Lie Groups Combinatorics



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram