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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Mixed norm $n$-widths
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by C. de Boor, R. DeVore and K. Höllig PDF
Proc. Amer. Math. Soc. 80 (1980), 577-583 Request permission

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
    C. de Boor and G. Fix, Spline approximation by quasi-interpolants, J. Approx. Theory 7 (1973), 19-45.
  • 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, DOI 10.1007/978-3-642-46066-1
  • E. Gluskin, On a problem concerning diameters, Soviet Math. Dokl. 15 (1974), 1592-1596.
  • 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
  • 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
  • Herbert John Ryser, Combinatorial mathematics, The Carus Mathematical Monographs, No. 14, Mathematical Association of America; distributed by John Wiley and Sons, Inc., New York, 1963. MR 0150048, DOI 10.5948/UPO9781614440147
  • 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
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 80 (1980), 577-583
  • MSC: Primary 41A46; Secondary 41A15, 41A25
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0587931-4
  • MathSciNet review: 587931