Chebyshev Splines and Kolmogorov Inequalities

By Sergey Bagdasarov

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 .

• Format: Paperback
• Language: English
• ISBN: 3034897812
• ISBN13: 9783034897815
• Release Date: October 2013
• Publisher: Birkhauser
• Length: 210 Pages
• Weight: 0.81 lbs.
• Dimensions: 0.5" x 6.7" x 9.6"