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Barycenters of extreme points in the cone of non-negative entire functions

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Abstract

In the cone of non-negative (on the real axis) entire functions, a certain simple functionf(x) is shown not to be the barycenter of any finite number of extreme functions. This is in contradistinction to S. Karlin's result that every non-negativepolynomial is the barycenter oftwo extreme ones.

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References

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Authors and Affiliations

  1. Department of Mathematics, 273 Altgeld Hall 1409 West Green Street, 61801, Urbana, Illinois

    Lee A. Rubel

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  1. Lee A. Rubel
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Research on this paper was partially supported by a grant from the National Science Foundation. The author thanks the Institut des Hautes Etudes Scientifiques for its hospitality during the preparation of this article.

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Rubel, L.A. Barycenters of extreme points in the cone of non-negative entire functions. Rend. Circ. Mat. Palermo 34, 245–248 (1985). https://doi.org/10.1007/BF02850699

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  • DOI: https://doi.org/10.1007/BF02850699

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