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- Author: Sergey Bagdasarov
- Publisher: Birkhäuser
- Year: 2013
- Pages: 210
- ISBN-10: 3034897812
- ISBN-13: 9783034897815
- Format: 17 x 24.4 x 1.2 cm, minkšti viršeliai
- Language: English
- SAVE -10% with code: EXTRA
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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 .
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- Author: Sergey Bagdasarov
- Publisher: Birkhäuser
- Year: 2013
- Pages: 210
- ISBN-10: 3034897812
- ISBN-13: 9783034897815
- Format: 17 x 24.4 x 1.2 cm, minkšti viršeliai
- Language: English English
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 .
Reviews