International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 1, Pages 91-101
Sign changes in linear combinations of derivatives and convolutions of Polya frequency functions
1Department of Mathematics, University of Pittsburgh, Pittsburgh 15213, Pennsylvania, USA
2Department of Statistics, Florida State University, Tallahassee 32306, Florida, USA
Received 5 September 1978
Copyright © 1979 Steven Nahmias and Frank Proschan. 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.
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.