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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Mixed norm $ n$-widths


Authors: C. de Boor, R. DeVore and K. Höllig
Journal: Proc. Amer. Math. Soc. 80 (1980), 577-583
MSC: Primary 41A46; Secondary 41A15, 41A25
MathSciNet review: 587931
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Abstract: Recently, the Soviet mathematicians R. Ismagilov [4], E. Gluskin [3] and B. Kashin [5] have obtained some deep and surprising results on n-widths for Sobolev spaces in the mixed norm case. In this note, we will give a new and simpler proof of Gluskin's result and show its connection with a certain classical combinatorial problem.


References [Enhancements On Off] (What's this?)

  • [1] C. de Boor and G. Fix, Spline approximation by quasi-interpolants, J. Approx. Theory 7 (1973), 19-45.
  • [2] Paul L. Butzer and Hubert Berens, Semi-groups of operators and approximation, Die Grundlehren der mathematischen Wissenschaften, Band 145, Springer-Verlag New York Inc., New York, 1967. MR 0230022 (37 #5588)
  • [3] E. Gluskin, On a problem concerning diameters, Soviet Math. Dokl. 15 (1974), 1592-1596.
  • [4] R. S. Ismagilov, Diameters of sets in normed linear spaces, and the approximation of functions by trigonometric polynomials, Uspehi Mat. Nauk 29 (1974), no. 3(177), 161–178 (Russian). MR 0407509 (53 #11284)
  • [5] B. S. Kašin, The widths of certain finite-dimensional sets and classes of smooth functions, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), no. 2, 334–351, 478 (Russian). MR 0481792 (58 #1891)
  • [6] Herbert John Ryser, Combinatorial mathematics, The Carus Mathematical Monographs, No. 14, Published by The Mathematical Association of America, 1963. MR 0150048 (27 #51)
  • [7] S. B. Stechkin, On the best approximation of given classes of functions by arbitrary polynomials, Usephi Mat. Nauk 9 (1954), no. 1, 133-134.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0587931-4
PII: S 0002-9939(1980)0587931-4
Keywords: Mixed norm n-widths, Sobolev spaces, combinatorics
Article copyright: © Copyright 1980 American Mathematical Society