Home > Research > Publications & Outputs > Moment-sequence transforms

Electronic data

  • 1610.05740

    Rights statement: © 2021 EMS Publishing House. All rights reserved

    Accepted author manuscript, 530 KB, PDF document

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


Text available via DOI:

View graph of relations

Moment-sequence transforms

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>31/05/2022
<mark>Journal</mark>Journal of the European Mathematical Society
Issue number9
Number of pages52
Pages (from-to)3109–3160
Publication StatusPublished
Early online date8/09/21
<mark>Original language</mark>English


We classify all functions which, when applied term by term, leave invariant the sequences of moments of positive measures on the real line. Rather unexpectedly, these functions are built of absolutely monotonic components, or reflections of them, with possible discontinuities at the endpoints. Even more surprising is the fact that functions preserving moments of three point masses must preserve moments of all measures. Our proofs exploit the semidefiniteness of the associated Hankel matrices and the complete monotonicity of the Laplace transforms of the underlying measures. As a byproduct, we characterize the entrywise transforms which preserve totally non-negative Hankel matrices, and those which preserve all totally non-negative matrices. The latter class is surprisingly rigid: such maps must be constant or linear. We also examine transforms in the multivariable setting, which reveals a new class of piecewise absolutely monotonic functions.

Bibliographic note

© 2021 EMS Publishing House. All rights reserved