Bivariate Truncated Moment Problems with an Extension of Multiplication Operators

Abstract

Recent results have been presented that confirm the commutativity of multiplication operators associated with moment sequences, thereby providing a resolution to the moment problem in certain settings. These results are formulated in terms of admissible index sets, which naturally subsume the well-studied (triangular) truncated moment problem. The present paper aims to investigate these findings in relation to foundational concepts predominantly employed in the truncated moment problem, called localizing matrices. In cases where the solution to a moment problem is difficult to characterize through specific properties of a moment sequence, it is often presented in the form of an algorithm. The primary objective of this paper is to improve upon a previously proposed algorithm in the context of bivariate truncated moment sequences. In particular, when the moment matrix exhibits a column relation, the recursively generated property can be exploited to simplify the algorithm to some extent. To enhance clarity and accessibility, illustrative examples are also provided.