n-Widths in Approximation Theory

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. Error...

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Bibliographic Details
Main Author: Pinkus, A.
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1985, 1985
Edition:1st ed. 1985
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I. Introduction
  • II. Basic Properties of n-Widths
  • 1. Properties of dn
  • 2. Existence of Optimal Subspaces for dn
  • 3. Properties of dn
  • 4. Properties of ?n
  • 5. Inequalities Between n-Widths
  • 6. Duality Between dn and dn
  • 7. n-Widths 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. n-Widths in Hilbert Spaces
  • 1. Introduction
  • 2. n-Widths of Compact Linear Operators
  • 3. n-Widths, with Constraints
  • 4. n-Widths of Compact Periodic Convolution Operators
  • 5. n-Widths of Totally Positive Operators in L2
  • 6. Certain Classes of Periodic Functions
  • Notes and References
  • V. Exact n-Widths of Integral Operators
  • 1. Introduction
  • 2. Exact n-Widths of K? in Lq and Kp in L1
  • 3. Exact n-Widths of K?r in Lq and Kpr in L1
  • 4. Exact n-Widths for Periodic Functions
  • 5. n-Widths of Rank n + 1 Kernels
  • Notes and References
  • VI. Matrices and n-Widths
  • 1. Introduction and General Remarks
  • 2. n-Widths of Diagonal Matrices
  • 3. n-Widths of Strictly Totally Positive Matrices
  • Notes and References
  • VII. Asymptotic Estimates for n-Widths 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. n-Widths of Analytic Functions
  • 1. Introduction
  • 2. n-Widths of Analytic Functions with Bounded mth Derivative
  • 3. n-Widths of Analytic Functions in H2
  • 4. n-Widths of Analytic Functions in H?
  • 5. n-Widths of a Class of Entire Functions
  • Notes and References
  • Glossary of Selected Symbols
  • Author Index