Chebyshev Splines and Kolmogorov Inequalities by Sergey Bagdasarov
Chebyshev Splines and Kolmogorov Inequalities

Chebyshev Splines and Kolmogorov Inequalities


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About the Book

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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Product Details
  • ISBN-13: 9783034897815
  • Publisher: Birkhauser
  • Publisher Imprint: Birkhauser
  • Edition: Softcover reprint of the original 1st ed. 1998
  • Language: English
  • Returnable: Y
  • Spine Width: 12 mm
  • Width: 170 mm
  • ISBN-10: 3034897812
  • Publisher Date: 03 Oct 2013
  • Binding: Paperback
  • Height: 244 mm
  • No of Pages: 210
  • Series Title: Operator Theory: Advances and Applications
  • Weight: 421 gr


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