Ebook: Orthogonal Polynomials: Theory and Practice
- Tags: Special Functions, Fourier Analysis, Computational Mathematics and Numerical Analysis
- Series: NATO ASI Series 294
- Year: 1990
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
This volume contains the Proceedings of the NATO Advanced Study Institute on "Orthogonal Polynomials and Their Applications" held at The Ohio State University in Columbus, Ohio, U.S.A. between May 22,1989 and June 3,1989. The Advanced Study Institute primarily concentrated on those aspects of the theory and practice of orthogonal polynomials which surfaced in the past decade when the theory of orthogonal polynomials started to experience an unparalleled growth. This progress started with Richard Askey's Regional Confer ence Lectures on "Orthogonal Polynomials and Special Functions" in 1975, and subsequent discoveries led to a substantial revaluation of one's perceptions as to the nature of orthogonal polynomials and their applicability. The recent popularity of orthogonal polynomials is only partially due to Louis de Branges's solution of the Bieberbach conjecture which uses an inequality of Askey and Gasper on Jacobi polynomials. The main reason lies in their wide applicability in areas such as Pade approximations, continued fractions, Tauberian theorems, numerical analysis, probability theory, mathematical statistics, scattering theory, nuclear physics, solid state physics, digital signal processing, electrical engineering, theoretical chemistry and so forth. This was emphasized and convincingly demonstrated during the presentations by both the principal speakers and the invited special lecturers. The main subjects of our Advanced Study Institute included complex orthogonal polynomials, signal processing, the recursion method, combinatorial interpretations of orthogonal polynomials, computational problems, potential theory, Pade approximations, Julia sets, special functions, quantum groups, weighted approximations, orthogonal polynomials associated with root systems, matrix orthogonal polynomials, operator theory and group representations.
Content:
Front Matter....Pages i-xi
Characterization Theorems for Orthogonal Polynomials....Pages 1-24
Orthogonal Polynomials in Coding Theory and Algebraic Combinatorics....Pages 25-53
Orthogonal Polynomials, Pad? Approximations and Julia Sets....Pages 55-97
The Three Term Recurrence Relation and Spectral Properties of Orthogonal Polynomials....Pages 99-114
On the Role of Orthogonal Polynomials on the Unit Circle in Digital Signal Processing Applications....Pages 115-133
A Survey on the Theory of Orthogonal System and Some Open Problems....Pages 135-146
Orthogonal Polynomials and Functional Analysis....Pages 147-161
Using Symbols Computer Algebraic Systems to Derive Formulas Involving Orthogonal Polynomials and Other Special Functions....Pages 163-179
Computational Aspects of Orthogonal Polynomials....Pages 181-216
The Recursion Method and the Schroedinger Equation....Pages 217-228
Birth and Death Processes and Orthogonal Polynomials....Pages 229-255
Orthogonal Polynomials in Connection with Quantum Groups....Pages 257-292
The Approximate Approach to Orthogonal Polynomials for Weights On (-?,?)....Pages 293-310
Orthogonal Polynomials Associated with Root Systems....Pages 311-318
Some Extensions of the Beta Integral and the Hypergeometric Function....Pages 319-344
Orthogonal Matrix Polynomials....Pages 345-362
Orthogonal Polynomials from a Complex Perspective....Pages 363-393
Nth Root Root Asymptotic Behavior of Orthonormal Polynomials....Pages 395-417
An Introduction to Group Representations and Orthogonal Polynomials....Pages 419-433
Asymptotics for Orthogonal Polynomials and Three-Term Recurrences....Pages 435-462
Content:
Front Matter....Pages i-xi
Characterization Theorems for Orthogonal Polynomials....Pages 1-24
Orthogonal Polynomials in Coding Theory and Algebraic Combinatorics....Pages 25-53
Orthogonal Polynomials, Pad? Approximations and Julia Sets....Pages 55-97
The Three Term Recurrence Relation and Spectral Properties of Orthogonal Polynomials....Pages 99-114
On the Role of Orthogonal Polynomials on the Unit Circle in Digital Signal Processing Applications....Pages 115-133
A Survey on the Theory of Orthogonal System and Some Open Problems....Pages 135-146
Orthogonal Polynomials and Functional Analysis....Pages 147-161
Using Symbols Computer Algebraic Systems to Derive Formulas Involving Orthogonal Polynomials and Other Special Functions....Pages 163-179
Computational Aspects of Orthogonal Polynomials....Pages 181-216
The Recursion Method and the Schroedinger Equation....Pages 217-228
Birth and Death Processes and Orthogonal Polynomials....Pages 229-255
Orthogonal Polynomials in Connection with Quantum Groups....Pages 257-292
The Approximate Approach to Orthogonal Polynomials for Weights On (-?,?)....Pages 293-310
Orthogonal Polynomials Associated with Root Systems....Pages 311-318
Some Extensions of the Beta Integral and the Hypergeometric Function....Pages 319-344
Orthogonal Matrix Polynomials....Pages 345-362
Orthogonal Polynomials from a Complex Perspective....Pages 363-393
Nth Root Root Asymptotic Behavior of Orthonormal Polynomials....Pages 395-417
An Introduction to Group Representations and Orthogonal Polynomials....Pages 419-433
Asymptotics for Orthogonal Polynomials and Three-Term Recurrences....Pages 435-462
....