论文信息 - Approximating weak Chebyshev subspaces by Chebyshev subspaces

Approximating weak Chebyshev subspaces by Chebyshev subspaces

We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties.

[1] L. Karlovitz,et al. Equioscillation under nonuniqueness in the approximation of continuous functions , 1970 .

[2] L. Schumaker. Spline Functions: Basic Theory , 1981 .

[3] I. J. Schoenberg. On smoothing operations and their generating functions , 1953 .

[4] A. Haar,et al. Die Minkowskische Geometrie und die Annäherung an stetige Funktionen , 1917 .

[5] Weakly interpolating subspaces , 1983 .

[6] G. Nürnberger. Approximation by Spline Functions , 1989 .

[7] E. Cheney. Introduction to approximation theory , 1966 .

[8] G. Meinardus. Approximation of Functions: Theory and Numerical Methods , 1967 .

[9] WEAK CHEBYSHEV SUBSPACES AND ALTERNATION , 1980 .

[10] Angus E. Taylor,et al. Introduction to functional analysis, 2nd ed. , 1986 .

[11] R. Zielke. Discontinuous Cebysev Systems , 1979 .

[12] I. Singer. Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces , 1970 .

[13] R. Phelps. Uniqueness of Hahn-Banach extensions and unique best approximation. , 1960 .

[14] P. J. Davis,et al. Introduction to functional analysis , 1958 .