Vol. 71, No. 2, 1977

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Total positivity and the exact n-width of certain sets in L1

Charles Anthony Micchelli and Allan Pinkus

Vol. 71 (1977), No. 2, 499–515
Abstract

In this paper we obtain the exact value of the L1 n-width, both in the sense of Kolmogorov and Gel’fand, and characterize optimal subspaces for the set

                 ∫
∑r           1                           r
𝒦r = {   ajkj(t)+  0 K (t,s)h(s) ds : (a1,⋅⋅⋅ ,ar) ∈ R ,∥h∥1 ≦ 1},
j=1

under certain total positivity assumptions on

{k1(t),⋅⋅⋅ ,kr(t),K (t,s)}.

A matrix analogue is also described.

Mathematical Subject Classification 2000
Primary: 41A45
Milestones
Received: 28 May 1976
Published: 1 August 1977
Authors
Charles Anthony Micchelli
Allan Pinkus