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140122  eng 
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a 9783642698941

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1 

a Pinkus, A.

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a nWidths in Approximation Theory
h Elektronische Ressource
c by A. Pinkus

250 


a 1st ed. 1985

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a Berlin, Heidelberg
b Springer Berlin Heidelberg
c 1985, 1985

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a X, 294 p
b online resource

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a I. Introduction  II. Basic Properties of nWidths  1. Properties of dn  2. Existence of Optimal Subspaces for dn  3. Properties of dn  4. Properties of ?n  5. Inequalities Between nWidths  6. Duality Between dn and dn  7. nWidths of Mappings of the Unit Ball  8. Some Relationships Between dn(T), dn(T) and ?n(T)  Notes and References  III. Tchebycheff Systems and Total Positivity  1. Tchebycheff Systems  2. Matrices  3. Kernels  4. More on Kernels  IV. nWidths in Hilbert Spaces  1. Introduction  2. nWidths of Compact Linear Operators  3. nWidths, with Constraints  4. nWidths of Compact Periodic Convolution Operators  5. nWidths of Totally Positive Operators in L2  6. Certain Classes of Periodic Functions  Notes and References  V. Exact nWidths of Integral Operators  1. Introduction  2. Exact nWidths of K? in Lq and Kp in L1  3. Exact nWidths of K?r in Lq and Kpr in L1  4. Exact nWidths for Periodic Functions  5. nWidths of Rank n + 1 Kernels  Notes and References  VI. Matrices and nWidths  1. Introduction and General Remarks  2. nWidths of Diagonal Matrices  3. nWidths of Strictly Totally Positive Matrices  Notes and References  VII. Asymptotic Estimates for nWidths of Sobolev Spaces  1. Introduction  2. Optimal Lower Bounds  3. Optimal Upper Bounds  4. Another Look at ?n(B1(r); L?)  Notes and References  VIII. nWidths of Analytic Functions  1. Introduction  2. nWidths of Analytic Functions with Bounded mth Derivative  3. nWidths of Analytic Functions in H2  4. nWidths of Analytic Functions in H?  5. nWidths of a Class of Entire Functions  Notes and References  Glossary of Selected Symbols  Author Index

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a Mathematical analysis

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a Calculus of Variations and Optimization

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a Control theory

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a Systems Theory, Control

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a Analysis

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a System theory

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a Mathematical optimization

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a Calculus of variations

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0 
7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

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a 10.1007/9783642698941

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u https://doi.org/10.1007/9783642698941?nosfx=y
x Verlag
3 Volltext

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a 3

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a My original introduction to this subject was through conservations, and ultimate ly joint work with C. A. Micchelli. I am grateful to him and to Profs. C. de Boor, E. W. Cheney, S. D. Fisher and A. A. Melkman who read various portions of the manuscript and whose suggestions were most helpful. Errors in accuracy and omissions are totally my responsibility. I would like to express my appreciation to the SERC of Great Britain and to the Department of Mathematics of the University of Lancaster for the year spent there during which large portions of the manuscript were written, and also to the European Research Office of the U.S. Army for its financial support of my research endeavors. Thanks are also due to Marion Marks who typed portions of the manuscript. Haifa, 1984 Allan Pinkus Table of Contents 1 Chapter I. Introduction . . . . . . . . Chapter II. Basic Properties of nWidths . 9 1. Properties of d • • • • • • • • • • 9 n 15 2. Existence of Optimal Subspaces for d • n n 17 3. Properties of d • • • • • • 20 4. Properties of b • • • • • • n 5. Inequalities Between nWidths 22 n 6. Duality Between d and d • • 27 n 7. nWidths of Mappings of the Unit Ball 29 8. Some Relationships Between dn(T), dn(T) and bn(T) . 32 37 Notes and References . . . . . . . . . . . . .
