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Technical Constructive Function Theory, Volume II: Approximation in Mean
Posted on 2010-04-14
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More I.P. Natanson, "Constructive Function Theory, Volume II: Approximation in Mean" Chapter I. THE SPACE L(z) 1. The Problem 2. The Weight Function. The Space L;(z) 3. Convergence in Mean 4. Classes of Functions Dense in L(z) Chapter II. ORTHOGONAL SYSTEMS 1. Orthogonality. Examples 2. The FOURIER Coefficients 3. Completeness and Closedness Chapter III. LINEARLY INDEPENDENT SYSTEMS OF FUNCTIONS 1. Linear Independence. The GRAM Determinant. The SCHMIDT Theorem 2. Approximation by Linearly Independent Functions 3. The MUNTZ Theorems Chapter IV. GENERAL PROPERTIES OF ORTHOGONAL POLYNOMIALS 1. Foundations 2. Roots of Orthogonal Polynomials. A Recursion Formula 3. Relation to the Theory of Continued Fractions 4. The CHRISTOFFEL-DARBOUX Formula. Convergence of Orthogonal Expansions. 5. Changing the Weight Function 74 Chapter V. THE LEGENDRE POLYNOMIALS 1. The RODRIGUES Formula 2. The Generating Function 3. The LAPLACE Integral 4. Expansions in Terms of LEGENDRE Polynomials Chapter VI. THE JACOBI POLYNOMIALS 1. Generalization of the RODRIGUES Formula 2. The Recursion Formula, Generating Function, and Differential Equation 3. Estimates of the JACOBI Polynomials. The Expansion Problem. 4. TCHEBYSHEFF Polynonmals of the Second Kind 5. The JACOBI Polynomials for a = !, = -! Chapter VII. THE MOMENT PROBLEM FOR FINITE INTERVALS 1. Formulation of the Problem 2. The Theorems of F. HAUSDORFF 3. Linear Functionals in C and L2 4. Positive Definite Sequences Chapter VIII. INFINITE INTERVALS 1. Introduction 2. The LAGUERRE Polynomials 3. The Generalized LAGUERRE Polynomials 4. The HERMITE Polynomials 5. The Moment Problem for Infinite Intervals 6. The FAVARD Theorem Bibliography Index Index of Symbols Download mirror Not all books ... appear on the homepage. In order not to miss many of them follow ebooks section (see top of each page on AH)
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