Vol. 89, No. 1, 1980

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Weak Chebyshev subspaces and alternation

Frank Richard Deutsch, Günther Nürnberger and Ivan Singer

Vol. 89 (1980), No. 1, 9–31
Abstract

Let T be a locally compact subset of R and C0(T) the space of continuous function which vanish at infinity. An n dimensional subspace G of C0(T) may possess one of the three alternation properties:

  1. For each f C0(T) which has a unique best approximation g0 G, f g0 has n + 1 alternating peak points;
  2. For each f C0(T), there exists a best approximation g0 G to f such that f g0 has n + 1 alternating peak points;
  3. For each f C0(T) and each best approximation g0 G to f,f g0 has n + 1 alternating peak points.

In this paper, for each i ∈{1,2,3} we give an intrinsic characterization of those subspaces G of C0(t) which have property (A-i).

Mathematical Subject Classification 2000
Primary: 41A50
Milestones
Received: 2 August 1978
Revised: 12 July 1979
Published: 1 July 1980
Authors
Frank Richard Deutsch
Günther Nürnberger
Ivan Singer