Optimal Recovery of Analytic Functions

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Nova Publishers, 2000 - Mathematics - 220 pages
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This book is devoted to the problems of optimal recovery on classes of analytic functions. Considered are the problems of optimal interpolation, differentiation, and quadrature formulas. Many problems of approximation theory may be considered as optimal recovery problems. Those problems are Kolmogorov's inequality and n-widths which are studied for the Hardy classes.
 

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Contents

Preface
5
Optimal Recovery Settings and General Results
11
12 Optimal Recovery of MultiValued Mappings
14
13 Optimal Recovery of Linear Functionals
20
14 Optimal Algorithms Using Fourier Coefficients
25
15 Notes and References
34
Optimal Recovery in Hp
37
22 The Periodic Case
40
36 Notes and References
121
Exact nWidths of Analytic Functions
123
41 Exact nWidths in Hp
124
42 Estimates of nWidths for Hp in Lq11
131
43 Exact nWidths of Periodic Functions
139
44 Estimations of nWidths in Hilbert Spaces
146
45 Diagonal Operators
155
46 HardySobolev and BergmanSobolev Classes
161

23 Countable Sets of Nodes
44
24 Optimal Nodes
51
25 Functions of Several Variables
65
26 Notes and References
81
Optimal Recovery of Derivatives
83
32 A General Case
87
33 The Periodic Case for the First Derivative
97
34 Noisy Information
104
35 Kolmogorov Inequalities
113
47 Notes and References
170
Quadrature Formulas
175
52 Optimal Quadrature Formulas
181
53 Estimates of Optimal Quadratures
189
54 Notes and References
198
Author Index
217
Subject Index
219
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