| Naslov: | The truncated univariate rational moment problem |
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| Avtorji: | ID Nailwal, Rajkamal (Avtor)
ID Zalar, Aljaž (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (927,53 KB)
MD5: A5AA139AD8FBA8CD59A97B78151C032F
 URL - Izvorni URL, za dostop obiščite https://www.sciencedirect.com/science/article/pii/S0024379524004816
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | Given a closed subset $K$ in ${\mathbb R}$, the rational $K$-truncated moment problem ($K$-RTMP) asks to characterize the existence of a positive Borel measure $\mu$, supported on $K$, such that a linear functional ${\mathcal L}$, defined on all rational functions of the form ${f \over q}$, 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 ▫$\mu$▫. The case of a compact set ▫$K$▫ was solved by Chandler in 1994, but there is no argument that ensures that $\mu$ vanishes on all real zeros of $q$. An obvious necessary condition for the solvability of the $K$-RTMP is that ${\mathcal L}$ is nonnegative on every $f$ satisfying $f|_K \ge 0$. If ${\mathcal L}$ is strictly positive on every $0 \ne f|_K \ge 0$, 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 ${\mathcal L}$ 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. |
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| Ključne besede: | truncated moment problem, rational truncated moment problem, representing measure, moment matrix, localizing moment matrix, preordering |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 13.12.2024 |
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| Leto izida: | 2025 |
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| Št. strani: | str. 280-301 |
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| Številčenje: | Vol. 708 |
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| PID: | 20.500.12556/DiRROS-21091  |
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| UDK: | 517.9 |
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| ISSN pri članku: | 0024-3795 |
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| DOI: | 10.1016/j.laa.2024.12.009 |
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| COBISS.SI-ID: | 219899139 |
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| Opomba: |
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| Datum objave v DiRROS: | 19.12.2024 |
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| Število ogledov: | 571 |
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| Število prenosov: | 312 |
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| Metapodatki: |    |
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