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Truncated Multi-index Sequences Have an Interpolating Measure
- Authors
- Choi, Hayoung; Yoo, Seonguk
- Issue Date
- Mar-2022
- Publisher
- 경북대학교 자연과학대학 수학과
- Keywords
- moment problem; interpolating measure; consistency; rank-one decomposition
- Citation
- Kyungpook Mathematical Journal, v.62, no.1, pp 107 - 118
- Pages
- 12
- Indexed
- SCOPUS
ESCI
KCI
- Journal Title
- Kyungpook Mathematical Journal
- Volume
- 62
- Number
- 1
- Start Page
- 107
- End Page
- 118
- ISSN
- 1225-6951
0454-8124
- Abstract
- In this note we observe that any truncated multi-index sequence has an interpolating measure supported in Euclidean space. It is well known that the consistency of a truncated moment sequence is equivalent to the existence of an interpolating measure for the sequence. When the moment matrix of a moment sequence is nonsingular, the sequence is naturally consistent; a proper perturbation to a given moment matrix enables us to confirm the existence of an interpolating measure for the moment sequence. We also illustrate how to find an explicit form of an interpolating measure for some cases.
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