Vol. 17, No. 3, 1966

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Generalized convexity cones

Zvi Ziegler

Vol. 17 (1966), No. 3, 561–580

We consider in this paper generalized convexity cones C(ψ1,n) with respect to an Extended Complete Tchebycheffian system {ψ1(x),n(x)}. These cones play a significant role in various areas of mathematics, such as moment theory, theory of approximation and interpolation, and theory of differential inequalities.

The properties of the cone C(ψ1,n) are investigated. In particular, the extreme ray problem is solved explicitly for this cone, and for the intersection of such cones. Several structural properties of the cones are then determined.

The cone dual to C(ψ1,n), which was introduced by S. Karlin and A. Novikoff is examined and a characterization of the cones which are dual to intersections of generalized convex cones is given. Some extensions of known theorems are given as applications.

Mathematical Subject Classification
Primary: 26.52
Received: 17 January 1965
Revised: 20 March 1965
Published: 1 June 1966
Zvi Ziegler