Author(s): I.P. Natanson
Edition: 1st
Publisher: Ungar
Year: 1965
Language: English
Pages: 174
Contents ......Page all_10102_to_00174.cpc0003.djvu
1. The Problem......Page all_10102_to_00174.cpc0005.djvu
2. The Weight Function. The Space L^2_{p(x)}......Page all_10102_to_00174.cpc0007.djvu
3. Convergence in Mean......Page all_10102_to_00174.cpc0009.djvu
4. Classes of Functions Dense in L^2_{p(x)}......Page all_10102_to_00174.cpc0013.djvu
1. Orthogonality. Examples......Page all_10102_to_00174.cpc0017.djvu
2. The Fourier Coefficients......Page all_10102_to_00174.cpc0021.djvu
3. Completeness and Closedness......Page all_10102_to_00174.cpc0027.djvu
1. Linear Independence. The Gram Determinant. The Schmidt Theorem......Page all_10102_to_00174.cpc0030.djvu
2. Approximation by Linearly Independent Functions......Page all_10102_to_00174.cpc0034.djvu
3. The Müntz Theorems......Page all_10102_to_00174.cpc0038.djvu
1. Foundations......Page all_10102_to_00174.cpc0043.djvu
2. Roots of Orthogonal Polynomials. A Recursion Formula......Page all_10102_to_00174.cpc0048.djvu
3. Relation to the Theory of Continued Fractions......Page all_10102_to_00174.cpc0056.djvu
4. The Christoffel-Darboux Formula. Convergence of Orthogonal Expansions.......Page all_10102_to_00174.cpc0064.djvu
5. Changing the Weight Function......Page all_10102_to_00174.cpc0072.djvu
1. The Rodrigues Formula......Page all_10102_to_00174.cpc0080.djvu
2. The Generating Function......Page all_10102_to_00174.cpc0086.djvu
3. The Laplace Integral......Page all_10102_to_00174.cpc0089.djvu
4. Expansions in Terms of Legendre Polynomials......Page all_10102_to_00174.cpc0092.djvu
1. Generalization of the Rodrigues Formula......Page all_10102_to_00174.cpc0100.djvu
2. The Recursion Formula, Generating Function, and Differential Equation......Page all_10102_to_00174.cpc0105.djvu
3. Estimates of the Jacobi Polynomials. The Expansion Problem.......Page all_10102_to_00174.cpc0107.djvu
4. Tchebysheff Polynomials of the Second Kind......Page all_10102_to_00174.cpc0112.djvu
5. The Jacobi Polynomials for \alpha = 1/2, \beta = -1/2......Page all_10102_to_00174.cpc0119.djvu
1. Formulation of the Problem......Page all_10102_to_00174.cpc0124.djvu
2. The Theorems of F. Hausdorff......Page all_10102_to_00174.cpc0128.djvu
3. Linear Functionals in C and L2......Page all_10102_to_00174.cpc0134.djvu
4. Positive Definite Sequences......Page all_10102_to_00174.cpc0140.djvu
1. Introduction......Page all_10102_to_00174.cpc0145.djvu
2. The Laguerre Polynomials......Page all_10102_to_00174.cpc0149.djvu
3. The Generalized Laguerre Polynomials......Page all_10102_to_00174.cpc0151.djvu
4. The Hermite Polynomials......Page all_10102_to_00174.cpc0154.djvu
5. The Moment Problem for Infinite Intervals......Page all_10102_to_00174.cpc0157.djvu
6. The Favard Theorem......Page all_10102_to_00174.cpc0165.djvu
Bibliography ......Page all_10102_to_00174.cpc0169.djvu
Index ......Page all_10102_to_00174.cpc0173.djvu
Index of Symbols ......Page all_10102_to_00174.cpc0174.djvu
