Chebyshev Splines and Kolmogorov Inequalities - Operator Theory: Advances and Applications - Sergey Bagdasarov - Kirjat - Springer Basel - 9783034897815 - torstai 3. lokakuuta 2013
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Chebyshev Splines and Kolmogorov Inequalities - Operator Theory: Advances and Applications Softcover reprint of the original 1st ed. 1998 edition

Sergey Bagdasarov

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Chebyshev Splines and Kolmogorov Inequalities - Operator Theory: Advances and Applications Softcover reprint of the original 1st ed. 1998 edition

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 .


210 pages, biography

Media Kirjat     Paperback Book   (Kirja pehmeillä kansilla ja liimatulla selällä)
Julkaisupäivämäärä torstai 3. lokakuuta 2013
ISBN13 9783034897815
Tuottaja Springer Basel
Sivujen määrä 210
Mitta 170 × 244 × 12 mm   ·   367 g
Kieli English  

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