Tchebycheff systems and best partial bases

Abstract

This is a contribution to the partial basis problem and, in particular, to the case where the basis elements are cosigns or consecutive powers cosines. We contribute also to the general theory of Tchebycheff systems to which the partial basis problem is strongly related. l Introduction* The partial basis problem was formulated and studied by J. T. Lewis, D. W. Tufts and the author in 1975 in connection with their study of optimization of multichannel processing. Let X be a normed linear space, let f,h u h 2 , ---,h N eX and let n be an integer, 1 <; n < N. For every sequence -{ k }? of integers, with 1 <;