Article
Kyungpook Mathematical Journal 2022; 62(1): 107-118
Published online March 31, 2022
Copyright © Kyungpook Mathematical Journal.
Truncated Multi-index Sequences Have an Interpolating Measure
Hayoung Choi, Seonguk Yoo*
Department of Mathematics, Kyungpook National University, Daegu 41566, Republic of Korea
e-mail : hayoung.choi@knu.ac.kr
Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Republic of Korea
e-mail : seyoo@gnu.ac.kr
Received: June 2, 2021; Revised: November 10, 2021; Accepted: November 15, 2021
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