Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1980-0587931-4
MathSciNet review: 587931
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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] P. L. Butzer and H. Berens, Semi-groups of operators and approximation, Springer-Verlag, Berlin, 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, Russian Math. Surveys 29 (1974), 169-186. MR 0407509 (53:11284)
  • [5] B. S. Kashin, The widths of certain finite dimensional sets and classes of smooth functions, Izv. Akad. Nauk SSSR, Ser. Mat. 41 (1977), 334-351. (Russian) MR 0481792 (58:1891)
  • [6] H. J. Ryser, Combinatorial mathematics, Carus Monographs, No. 14, 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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 41A46, 41A15, 41A25

Retrieve articles in all journals with MSC: 41A46, 41A15, 41A25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0587931-4
Keywords: Mixed norm n-widths, Sobolev spaces, combinatorics
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society