Discrete and continuous boundary problems / F. V. Atkinson.

Format:

Book

Author/Creator:

Atkinson, F. V.

Series:

Mathematics in science and engineering ; v. 8.

Mathematics in science and engineering ; v. 8

Language:

English

Subjects (All):

Boundary value problems.

Differential equations.

Physical Description:

1 online resource (xiv, 570 pages)

Place of Publication:

New York : Academic Press, 1964.

Language Note:

English

Summary:

Discrete and continuous boundary problems

Contents:

Front Cover; Mathematics in Science and Engineering; Discrete and Continuous Boundary Problems; Copyright Page; Preface; Contents; Introduction; 0.1. Difference and Differential Equations; 0.2. The Invariance Property; 0.3. The Scalar Case; 0.4. All-Pass Transfer Functions; 0.5. Inverse Problems; 0.6. The General Orthogonal Case; 0.7. The Three-Term Recurrence Formula; 0.8. The 2-by-2 Symplectic Case; Chapter 1. Boundary Problems for Rational Functions; 1.1. Finite Fourier Series; I .2. The Boundary Problem; 1.3. Oscillation Properties; 1.4. Eigenfunctions and Orthogonality

1.5. The Spectral Function; 1.6. The Characteristic Function; 1.7. The First Inverse Problem; 1.8. The Second Inverse Problem; 1.9. Moment Characterization of the Spectral Function; 1.10. Solution of a Moment Problem; Chapter 2. The Infinite Discrete Case; 2.1. A Limiting Procedure; 2.2. Convergence of the Fundamental Solution; 2.3. Convergence of the Spectral Function; 2.4. Convergence of the Characteristic Function; 2.5. Eigenvalues and Orthogonality; 2.6. Orthogonality and Expansion Theorem; 2.7. A Continuous Spectrum; 2.8. Moment and Interpolation Problem; 2.9. A Mixed Boundary Problem

2.10. A Mixed Expansion Problem; 2.11. Further Boundary Problems; Chapter 3. Discrete Linear Problems; 3.1. Problems Linear in the Parameter; 3.2. Reduction to Canonical Form; 3.3. The Real Axis Case; 3.4. The Unit Circle Case; 3.5. The Real 2-by-2 Case; 3.6. The 2-by-2 Unit Circle Case; 3.7. The Boundary Problem on the Real Axis; 3.8. The Boundary Problem on the Unit Circle; Chapter 4. Finite Orthogonal Polynomials; 4.1. The Recurrence Relation; 4.2. Lagrange-Type Identities; 4.3. Oscillatory Properties; 4.4. Orthogonality; 4.5. Spectral and Characteristic Functions

4.6. The First Inverse Spectral Problem; 4.7. The Second Inverse Spectral Problem; 4.8. Spectral Functions in General; 4.9. Some Continuous Spectral Functions; Chapter 5. Orthogonal Polynomials The Infinite Case; 5.1. Limiting Boundary Problems; 5.2. Spectral Functions; 5.3. Orthogonality and Expansion Theorem; 5.4. Nesting Circle Analysis; 5.5. Limiting Spectral Functions; 5.6. Solutions of Summable Square; 5.7. Eigenvalues in the Limit-Circle Case; 5.8. Limit-Circle, Limit-Point Tests; 5.9. Moment Problem; 5.10. The Dual Expansion Theorem; Chapter 6. Matrix Methods for Polynomials

6.1. Orthogonal Polynomials as Jacobi Determinants; 6.2. Expansion Theorems, Periodic Boundary Conditions; 6.3. Another Method for Separation Theorems; 6.4. The Green's Function; 6.5. A Reactance Theorem; 6.6. Polynomials with Matrix Coefficients; 6.7. Oscillatory Properties; 6.8. Orthogonality; 6.9. Polynomials in Several Variables; 6.10. The Multi-Parameter Oscillation Theorem; 6.11. Multi-Dimensional Orthogonality; Chapter 7. Polynomials Orthogonal on the Unit Circle; 7.1. The Recurrence Relation; 7.2. The Boundary Problem; 7.3. Orthogonality; 7.4. The Recurrence Formulas Deduced from the Orthogonality

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-282-28919-5

9786612289194

0-08-095516-9

OCLC:

316566890