Abstract
The approximation problem is: Given f~ C(X), to find a coefficient vector A* minimizing e(A) = Ilf F(A, .)\I over A E 9’. Such a coefficient vector A* is called best and &A*, .) is called a best approximation tofon X. 1,~ is a transformation operator. The first study of transformations was that of the author [2], who studied transformations of ordinary rational functions on an interval. Kaufman and Belford [6] have studied transformations of alternating families. Williams [9] has studied some special cases of transformations of Haar subspaces on an interval.
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