Chebyshev Splines and Kolmogorov Inequalities (Operator Theory: Advances and Applications)

Bagdasarov, Sergey

Springer Basel（2013/10発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 210 p.
• 言語 ENG
• 商品コード 9783034897815
• DDC分類 511.4

Full Description

Since the introduction of the functional classes HW (lI) and WT HW (lI) and their peri- odic analogs Hw (1I') and ‾ (1I'), defined by a concave majorant w of functions and their rth derivatives, many researchers have contributed to the area of ex- tremal problems and approximation of these classes by algebraic or trigonometric polynomials, splines and other finite dimensional subspaces. In many extremal problems in the Sobolev class W‾ (lI) and its periodic ana- log W‾ (1I') an exceptional role belongs to the polynomial perfect splines of degree r, i.e. the functions whose rth derivative takes on the values -1 and 1 on the neighbor- ing intervals. For example, these functions turn out to be extremal in such problems of approximation theory as the best approximation of classes W‾ (lI) and W‾ (1I') by finite-dimensional subspaces and the problem of sharp Kolmogorov inequalities for intermediate derivatives of functions from W‾. Therefore, no advance in the T exact and complete solution of problems in the nonperiodic classes W HW could be expected without finding analogs of polynomial perfect splines in WT HW .