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  • one-sided_PFF_v7

    Rights statement: This is the author’s version of a work that was accepted for publication in Applied and Computational Harmonic Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied and Computational Harmonic Analysis, 373, 4-5, 2022 DOI: 10.1016/S0370-1573(02)00269-7

    Accepted author manuscript, 437 KB, PDF document

    Embargo ends: 15/04/24

    Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License


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Hirschman-Widder densities

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>30/09/2022
<mark>Journal</mark>Applied and Computational Harmonic Analysis
Number of pages30
Pages (from-to)396-425
Publication StatusPublished
Early online date12/04/22
<mark>Original language</mark>English


Hirschman and Widder introduced a class of Pólya frequency functions given by linear combinations of one-sided exponential functions. The members of this class are probability densities, and the class is closed under convolution but not under pointwise multiplication. We show that, generically, a polynomial function of such a density is a Pólya frequency function only if the polynomial is a homothety, and also identify a subclass for which each positive-integer power is a Pólya frequency function. We further demonstrate connections between the Maclaurin coefficients, the moments of these densities, and the recovery of the density from finitely many moments, via Schur polynomials.