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Title:The truncated univariate rational moment problem
Authors:ID Nailwal, Rajkamal (Author)
ID Zalar, Aljaž (Author)
Files:.pdf PDF - Presentation file, download (927,53 KB)
MD5: A5AA139AD8FBA8CD59A97B78151C032F
 
URL URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0024379524004816
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract:Given a closed subset K in R, the rational K-truncated moment problem (K-RTMP) asks to characterize the existence of a positive Borel measure μ, supported on K, such that a linear functional L, defined on all rational functions of the form fq, where q is a fixed polynomial with all real zeros of even order and f is any real polynomial of degree at most 2k, is an integration with respect to μ. The case of a compact set K was solved by Chandler in 1994, but there is no argument that ensures that μ vanishes on all real zeros of q. An obvious necessary condition for the solvability of the K-RTMP is that L is nonnegative on every f satisfying f|K≥0. If L is strictly positive on every 0≠f|K≥0, we add the missing argument in Chadler's solution and also bound the number of atoms in a minimal representing measure. We show by an example that nonnegativity of L is not sufficient and add the missing conditions to the solution. We also solve the K-RTMP for unbounded K and derive the solutions to the strong truncated Hamburger moment problem and the truncated moment problem on the unit circle as special cases.
Keywords:truncated moment problem, rational truncated moment problem, representing measure, moment matrix, localizing moment matrix, preordering
Publication status:Published
Publication version:Version of Record
Publication date:13.12.2024
Year of publishing:2025
Number of pages:str. 280-301
Numbering:Vol. 708
PID:20.500.12556/DiRROS-21091 New window
UDC:517.9
ISSN on article:0024-3795
DOI:10.1016/j.laa.2024.12.009 New window
COBISS.SI-ID:219899139 New window
Note:
Publication date in DiRROS:19.12.2024
Views:229
Downloads:83
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NAILWAL, Rajkamal and ZALAR, Aljaž, 2025, The truncated univariate rational moment problem. Linear algebra and its applications [online]. 2025. Vol. 708, p. 280–301. [Accessed 21 April 2025]. DOI 10.1016/j.laa.2024.12.009. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=21091
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Record is a part of a journal

Title:Linear algebra and its applications
Shortened title:Linear algebra appl.
Publisher:Elsevier
ISSN:0024-3795
COBISS.SI-ID:1119247 New window

Document is financed by a project

Funder:ARIS - Slovenian Research and Innovation Agency
Project number:P1-0288
Name:Algebra in njena uporaba
Funder:ARIS - Slovenian Research and Innovation Agency
Project number:J1-50002
Name:Realna algebraična geometrija v matričnih spremenljivkah
Funder:ARIS - Slovenian Research and Innovation Agency
Project number:J1-60011

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

Language:Slovenian
Keywords:prirezani momentni problem, racionalni prirezani momentni problem, reprezentirajoča mera, momentna matrika, lokalizirajoča momentna matrika, predureditev


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