Chebyshev Splines and Kolmogorov Inequalities

Sergey Bagdasarov

ISBN 10: 3034897812 / ISBN 13: 9783034897815

Published by Birkhäuser Basel, 2013

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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 .

Seller Inventory # 9783034897815

Bibliographic Details

• Title: Chebyshev Splines and Kolmogorov Inequalities
• Publisher: Birkhäuser Basel
• Publication Date: 2013
• Language: English
• ISBN 10: 3034897812
• ISBN 13: 9783034897815
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 244W x 170H x 13D millimeters 244 millimeters width by 170 millimeters height by 13 millimeters depth
• Weight: 402 grams

About this title

Synopsis

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 .