Optimal Approximation of Periodic Analytic Functions with Integrable Boundary Values
✍ Scribed by Klaus Wilderotter
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 465 KB
- Volume
- 84
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
✦ Synopsis
Let S=[z # C: |Im(z)|<;] be a strip in the complex plane. H q , 1 q< , denotes the space of functions, which are analytic and 2?-periodic in S, real-valued on the real axis, and possess q-integrable boundary values. Let + be a positive measure on [0, 2?] and L p (+) be the corresponding Lebesgue space of periodic real-valued functions on the real axis. The even dimensional Kolmogorov, Gel'fand, and linear widths of the unit ball of H q in L p ( +) are determined exactly, when 1 p q< or when 2=q<p< and ; is sufficiently large. It is shown that all three n-widths coincide and a characterization of the widths in terms of Blaschke products is established.