Constructive Function Theory. Volume III: Interpolation and Approximation Quadratures - ISBN:0804446970

Constructive Function Theory. Volume III: Interpolation and Approximation Quadratures

Date: 23 April 2011, 23:49

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Chapter I. VARIOUS METHODS OF INTERPOLATION
1. The Problem
2 The LAGRANGE Formula
3. A Rearrangement of the LAGRANGE Formula - NEWTON'S Formula
4. Interpolation with Multiple Nodes
5. Trigonometric Interpolation
Chapter II. THEOREMS OF NEGATIVE CHARACTER
1. The Theorems of S. N. BERNSTEIN and G. FABER
2. The BERNSTEIN Example
3. An Example Due to MARCINKIEWICZ
Chapter III. THE CONVERGENCE OF INTERPOLATION PROCESSES
1. The Role of the Function An(X)
2. The Theorems of GRUNWALD and TURAN
3. Convergence in Mean
4. The FEJER Interpolation Process
5. Generalization of the Preceding Results
6. Normal Matrices
Chapter IV. SEVERAL CONVERGENCE PROCESSES RELATED TO INTERPOLATION
1. The First BERNSTEIN Procedure
2. The Second BERNSTEIN Procedure
3. A Theorem of S. M. LOSINSKI and the Method of S.J. RAPPOPORT
4. The Third BERNSTEIN Procedure
5. Certain General Properties of Summation Formulas
Chapter V. APPROXIMATION QUADRATURES
1. The Problem
2. The Remainder in the Quadrature Formula
3. Quadratures of Gaussian Type
4. Special Quadratures of Gaussian Type
Chapter VI. SUPPLEMENT TO THE THEORY OF APPROXIMATION QUADRATURES
1. The General Quadrature Process and its Convergence
2. Quadratures with Positive Coefficients
3. A Theorem Due to R. O. KUSMIN
4. The TCHEBYSHEFF Problem and a BERNSTEIN Theorem
5. The POSSE Theorem
Appendix 1. STIRLING'S FORMULA
Appendix 2. ON THE MUNTZ THEOREMS
Appendix 3. THE THEOREMS OF S.M. LOSINSKI-F.I. KHARSHILADZE AND V.F. NIKOLAEV
Bibliography 170
Index 175
Index of Symbols 176

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