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http://dx.doi.org/10.5666/KMJ.2022.62.1.107

Truncated Multi-index Sequences Have an Interpolating Measure  

Choi, Hayoung (Department of Mathematics, Kyungpook National University)
Yoo, Seonguk (Department of Mathematics Education and RINS, Gyeongsang National University)
Publication Information
Kyungpook Mathematical Journal / v.62, no.1, 2022 , pp. 107-118 More about this Journal
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.
Keywords
moment problem; interpolating measure; consistency; rank-one decomposition;
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