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International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 1, Pages 91-101
http://dx.doi.org/10.1155/S0161171279000090

Sign changes in linear combinations of derivatives and convolutions of Polya frequency functions

1Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15213, USA
2Department of Statistics, Florida State University, Tallahassee, Florida 32306, USA

Received 5 September 1978

Copyright © 1979 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We obtain upper bounds on the number of sign changes of linear combinations of derivatives and convolutions of Polya frequency functions using the variation diminishing properties of totally positive functions. These constitute extensions of earlier results of Karlin and Proschan.