Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On $ n$-widths in $ L\sp{\infty }$

Authors: Charles A. Micchelli and Allan Pinkus
Journal: Trans. Amer. Math. Soc. 234 (1977), 139-174
MSC: Primary 41A45
MathSciNet review: 0487187
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The n-width in $ {L^\infty }$ of certain sets determined by matrices and integral operators is determined. The notion of total positivity is essential in the analysis.

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

  • [1] Charles K. Chui and Philip W. Smith, Some nonlinear spline approximation problems related to 𝑁-widths, J. Approximation Theory 13 (1975), 421–430. Collection of articles dedicated to G. G. Lorentz on the occasion of his sixty-fifth birthday, IV. MR 0370023
  • [2] Samuel Karlin, Total positivity. Vol. I, Stanford University Press, Stanford, Calif, 1968. MR 0230102
  • [3] Samuel Karlin and Allan Pinkus, Oscillation properties of generalized characteristic polynomials for totally positive and positive definite matrices, Linear Algebra and Appl. 8 (1974), 281–312. MR 0342538
  • [4] Samuel Karlin and Allan Pinkus, Interpolation by splines with mixed boundary conditions, Studies in spline functions and approximation theory, Academic Press, New York, 1976, pp. 305–325. MR 0481731
  • [5] A. Kolmogoroff, Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse, Ann. of Math. (2) 37 (1936), no. 1, 107–110 (German). MR 1503273, 10.2307/1968691
  • [6] Avraham A. Melkman, Interpolation by splines satisfying mixed boundary conditions, Israel J. Math. 19 (1974), 369–381. MR 0372475
  • [7] Charles A. Micchelli, Best 𝐿¹ approximation by weak Chebyshev systems and the uniqueness of interpolating perfect splines, J. Approximation Theory 19 (1977), no. 1, 1–14. MR 0454479
  • [8] Samuel Karlin, Charles A. Micchelli, Allan Pinkus, and I. J. Schoenberg (eds.), Studies in spline functions and approximation theory, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0393934
  • [9] Ivan Singer, Best approximation in normed linear spaces by elements of linear subspaces, Translated from the Romanian by Radu Georgescu. Die Grundlehren der mathematischen Wissenschaften, Band 171, Publishing House of the Academy of the Socialist Republic of Romania, Bucharest; Springer-Verlag, New York-Berlin, 1970. MR 0270044
  • [10] V. M. Tihomirov, Best methods of approximation and interpolation of differentiable functions in the space 𝐶[-1,1]., Mat. Sb. (N.S.) 80 (122) (1969), 290–304 (Russian). MR 0256043

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 41A45

Retrieve articles in all journals with MSC: 41A45

Additional Information

Article copyright: © Copyright 1977 American Mathematical Society