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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Chebyshev Splines and Kolmogorov Inequalities

Chebyshev Splines and Kolmogorov Inequalities

Bagdasarov, Sergey

Paperback

Series: Operator Theory: Advances and Applications, Book 105

CalculusGeneral Mathematics

ISBN10: 3034897812
ISBN13: 9783034897815
Publisher: Springer Nature
Published: Oct 3 2013
Pages: 210
Weight: 0.81
Height: 0.48 Width: 6.69 Depth: 9.61
Language: 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 .

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