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Sign changes in linear combinations of derivatives and convolutions of Polya frequency functionsDOI: 10.1155/s0161171279000090 Keywords: Polya frequency functions , sign changes , derivatives , convolutions , total positivity , variation diminishing property , linear combinations , sign regular functions. 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.
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