Chebyshev Splines and Kolmogorov Inequalities:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser Basel
1998
|
| Series: | Operator Theory Advances and Applications
105 |
| Subjects: | |
| Online Access: | Volltext |
| Item 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 |
| Physical Description: | 1 Online-Ressource (XIII, 210 p) |
| ISBN: | 9783034888080 9783034897815 |
| DOI: | 10.1007/978-3-0348-8808-0 |
Staff View
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| spelling | Bagdasarov, Sergey K. Verfasser aut Chebyshev Splines and Kolmogorov Inequalities by Sergey K. Bagdasarov Basel Birkhäuser Basel 1998 1 Online-Ressource (XIII, 210 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory Advances and Applications 105 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 Mathematics Mathematics, general Mathematik Approximation (DE-588)4002498-2 gnd rswk-swf Extremwert (DE-588)4137272-4 gnd rswk-swf Čebyšev-Spline (DE-588)4528418-0 gnd rswk-swf Kolmogorov-Ungleichung (DE-588)4528419-2 gnd rswk-swf Extremwert (DE-588)4137272-4 s Approximation (DE-588)4002498-2 s Kolmogorov-Ungleichung (DE-588)4528419-2 s Čebyšev-Spline (DE-588)4528418-0 s 1\p DE-604 https://doi.org/10.1007/978-3-0348-8808-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bagdasarov, Sergey K. Chebyshev Splines and Kolmogorov Inequalities Mathematics Mathematics, general Mathematik Approximation (DE-588)4002498-2 gnd Extremwert (DE-588)4137272-4 gnd Čebyšev-Spline (DE-588)4528418-0 gnd Kolmogorov-Ungleichung (DE-588)4528419-2 gnd |
| subject_GND | (DE-588)4002498-2 (DE-588)4137272-4 (DE-588)4528418-0 (DE-588)4528419-2 |
| title | Chebyshev Splines and Kolmogorov Inequalities |
| title_auth | Chebyshev Splines and Kolmogorov Inequalities |
| title_exact_search | Chebyshev Splines and Kolmogorov Inequalities |
| title_full | Chebyshev Splines and Kolmogorov Inequalities by Sergey K. Bagdasarov |
| title_fullStr | Chebyshev Splines and Kolmogorov Inequalities by Sergey K. Bagdasarov |
| title_full_unstemmed | Chebyshev Splines and Kolmogorov Inequalities by Sergey K. Bagdasarov |
| title_short | Chebyshev Splines and Kolmogorov Inequalities |
| title_sort | chebyshev splines and kolmogorov inequalities |
| topic | Mathematics Mathematics, general Mathematik Approximation (DE-588)4002498-2 gnd Extremwert (DE-588)4137272-4 gnd Čebyšev-Spline (DE-588)4528418-0 gnd Kolmogorov-Ungleichung (DE-588)4528419-2 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Approximation Extremwert Čebyšev-Spline Kolmogorov-Ungleichung |
| url | https://doi.org/10.1007/978-3-0348-8808-0 |
| work_keys_str_mv | AT bagdasarovsergeyk chebyshevsplinesandkolmogorovinequalities |