Author | Pinkus, Allan. author |
---|---|
Title | n-Widths in Approximation Theory [electronic resource] / by Allan Pinkus |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1985 |
Connect to | http://dx.doi.org/10.1007/978-3-642-69894-1 |
Descript | X, 294 p. online resource |
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