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
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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Hirschman-Widder densities
AU - Belton, Alexander
AU - Guillot, Dominique
AU - Khare, Apoorva
AU - Putinar, Mihai
PY - 2022/9/30
Y1 - 2022/9/30
N2 - 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.
AB - 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.
U2 - 10.1016/j.acha.2022.04.002
DO - 10.1016/j.acha.2022.04.002
M3 - Journal article
VL - 60
SP - 396
EP - 425
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
SN - 1063-5203
ER -