The moment problem on curves with bumps

David P. Kimsey; Mihai Putinar

doi:10.1007/s00209-020-02633-2

The moment problem on curves with bumps

David P. Kimsey, Mihai Putinar

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the data. Except some fortunate configurations, in higher dimensions there are no non-negativity criteria for the power moments of a measure to be supported by a prescribed closed set. We combine two well studied fortunate situations, specifically a class of curves in two dimensions classified by Scheiderer and Plaumann, and compact, basic semi-algebraic sets, with the aim at enlarging the realm of geometric shapes on which the power moment problem is accessible and solvable by non-negativity certificates.

Original language	English
Pages (from-to)	935-942
Number of pages	8
Journal	Mathematische Zeitschrift
Volume	298
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-020-02633-2
State	Published - 1 Aug 2021
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00209-020-02633-2

Cite this

@article{ed05d75eb33d4ee098ed1b0f92a28a44,

title = "The moment problem on curves with bumps",

abstract = "The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the data. Except some fortunate configurations, in higher dimensions there are no non-negativity criteria for the power moments of a measure to be supported by a prescribed closed set. We combine two well studied fortunate situations, specifically a class of curves in two dimensions classified by Scheiderer and Plaumann, and compact, basic semi-algebraic sets, with the aim at enlarging the realm of geometric shapes on which the power moment problem is accessible and solvable by non-negativity certificates.",

author = "Kimsey, {David P.} and Mihai Putinar",

note = "Publisher Copyright: {\textcopyright} 2020, The Author(s).",

year = "2021",

month = aug,

day = "1",

doi = "10.1007/s00209-020-02633-2",

language = "English",

volume = "298",

pages = "935--942",

journal = "Mathematische Zeitschrift",

issn = "0025-5874",

publisher = "Springer New York",

number = "3-4",

}

TY - JOUR

T1 - The moment problem on curves with bumps

AU - Kimsey, David P.

AU - Putinar, Mihai

PY - 2021/8/1

Y1 - 2021/8/1

N2 - The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the data. Except some fortunate configurations, in higher dimensions there are no non-negativity criteria for the power moments of a measure to be supported by a prescribed closed set. We combine two well studied fortunate situations, specifically a class of curves in two dimensions classified by Scheiderer and Plaumann, and compact, basic semi-algebraic sets, with the aim at enlarging the realm of geometric shapes on which the power moment problem is accessible and solvable by non-negativity certificates.

AB - The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the data. Except some fortunate configurations, in higher dimensions there are no non-negativity criteria for the power moments of a measure to be supported by a prescribed closed set. We combine two well studied fortunate situations, specifically a class of curves in two dimensions classified by Scheiderer and Plaumann, and compact, basic semi-algebraic sets, with the aim at enlarging the realm of geometric shapes on which the power moment problem is accessible and solvable by non-negativity certificates.

UR - http://www.scopus.com/inward/record.url?scp=85094146197&partnerID=8YFLogxK

U2 - 10.1007/s00209-020-02633-2

DO - 10.1007/s00209-020-02633-2

M3 - Article

AN - SCOPUS:85094146197

SN - 0025-5874

VL - 298

SP - 935

EP - 942

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

The moment problem on curves with bumps

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this