On determinacy/indeterminacy of Moment Problems
Erik Ald\'en
TL;DR
This paper explores conditions for determinacy and indeterminacy in strong moment problems, focusing on Stieltjes and Hamburger cases, and summarizes related prior research with new theorems for general distribution functions.
Contribution
It provides a comprehensive analysis of strong moment problems, including new theorems on indeterminacy for broad classes of distribution functions.
Findings
Criteria for determinacy and indeterminacy established
Theorems for strong moment problems generalized to all distribution functions
Summary of prior work with new insights into moment problem solutions
Abstract
This paper treat determinacy of strong moment problems in part I and indeterminacy of strong moment problems in part II. This paper is a summary of the following papers: [1] Ald\'en. E., Determinacy of Strong Moment Problems. [2] On Indeterminacy of Strong Moment Problems. [3] Indeterminacy of Strong Moment Problems. This paper will treat determinacy/indeterminacy of the strong Stieltjes and Hamburger moment problems, part I. Indeterminacy, part II, for certain class of distribution functions. We conclude by proving a theorem for indeterminacy of the strong problems above for general distribution functions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSpectral Theory in Mathematical Physics · Mathematical functions and polynomials · Matrix Theory and Algorithms