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Moment-sequence transforms

Research output: Working paper

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Moment-sequence transforms. / Belton, Alexander; Guillot, Dominique; Khare, Apoorva et al.
Arxiv, 2016.

Research output: Working paper

Harvard

Belton, A, Guillot, D, Khare, A & Putinar, M 2016 'Moment-sequence transforms' Arxiv. <https://arxiv.org/abs/1610.05740>

APA

Belton, A., Guillot, D., Khare, A., & Putinar, M. (2016). Moment-sequence transforms. Arxiv. https://arxiv.org/abs/1610.05740

Vancouver

Belton A, Guillot D, Khare A, Putinar M. Moment-sequence transforms. Arxiv. 2016 Oct 27.

Author

Belton, Alexander ; Guillot, Dominique ; Khare, Apoorva et al. / Moment-sequence transforms. Arxiv, 2016.

Bibtex

@techreport{8feaa241a3854c829b1fee9090b95fde,
title = "Moment-sequence transforms",
abstract = "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. We also examine transformers in the multivariable setting, which reveals a new class of piecewise absolutely monotonic functions.",
author = "Alexander Belton and Dominique Guillot and Apoorva Khare and Mihai Putinar",
year = "2016",
month = oct,
day = "27",
language = "English",
publisher = "Arxiv",
type = "WorkingPaper",
institution = "Arxiv",

}

RIS

TY - UNPB

T1 - Moment-sequence transforms

AU - Belton, Alexander

AU - Guillot, Dominique

AU - Khare, Apoorva

AU - Putinar, Mihai

PY - 2016/10/27

Y1 - 2016/10/27

N2 - 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. We also examine transformers in the multivariable setting, which reveals a new class of piecewise absolutely monotonic functions.

AB - 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. We also examine transformers in the multivariable setting, which reveals a new class of piecewise absolutely monotonic functions.

M3 - Working paper

BT - Moment-sequence transforms

PB - Arxiv

ER -