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Hirschman–Widder densities

Lookup NU author(s): Professor Mihai Putinar

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Abstract

© 2022 Elsevier Inc. 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.

Publication metadata

Author(s): Belton A, Guillot D, Khare A, Putinar M

Publication type: Article

Publication status: Published

Journal: Applied and Computational Harmonic Analysis

Year: 2022

Volume: 60

Pages: 396-425

Print publication date: 01/09/2022

Online publication date: 12/04/2022

Acceptance date: 08/04/2022

ISSN (print): 1063-5203

ISSN (electronic): 1096-603X

Publisher: Academic Press

URL: https://doi.org/10.1016/j.acha.2022.04.002

DOI: 10.1016/j.acha.2022.04.002

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