Hirschman-Widder densities

Belton, Alexander and Guillot, Dominique and Khare, Apoorva and Putinar, Mihai (2022) Hirschman-Widder densities. Applied and Computational Harmonic Analysis, 60. pp. 396-425. ISSN 1063-5203

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Abstract

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.

Item Type:
Journal Article
Journal or Publication Title:
Applied and Computational Harmonic Analysis
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2604
Subjects:
ID Code:
168835
Deposited By:
Deposited On:
13 Apr 2022 15:35
Refereed?:
Yes
Published?:
Published
Last Modified:
14 May 2022 02:27