On weightedLpintegrability and approximation of trigonometric series
β Scribed by Baorong Wei; Dansheng Yu
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 113 KB
- Volume
- 25
- Category
- Article
- ISSN
- 1573-8175
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Many approximation methods in C 2? may be generated via a certain function . # C [0, 1] with .(0)=1, .(1)=0. The function . j (t)=cos( j&1Γ2) ?t ( j # N) generates the Rogosinski approximation method [N. K. Bari, ``A Treatise on Trigonometric Series,'' Vols. I, II, Pergamon Press, New York, 1964]. O
New integrability and L 1 -convergence classes for the r-times differentiated trigonometric series kβZ (ik) r c k e ikx are derived using known results on integrability and L 1 -convergence of trigonometric series. These classes, Theorems 1 and 2, subsume all known integrability and L 1 -convergence