{"paper":{"title":"On certain non-unique solutions of the Stieltjes moment problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.FA","authors_text":"A. Horzela (IFJ-PAN - Polish Academy of Sciences), A. I. Solomon, G. H. E. Duchamp (LIPN), K. A. Penson (LPTMC), P. Blasiak (IFJ-PAN - Polish Academy of Sciences)","submitted_at":"2009-09-26T07:48:35Z","abstract_excerpt":"We construct explicit solutions of a number of Stieltjes moment problems based on moments of the form ${\\rho}_{1}^{(r)}(n)=(2rn)!$ and ${\\rho}_{2}^{(r)}(n)=[(rn)!]^{2}$, $r=1,2,...$, $n=0,1,2,...$, \\textit{i.e.} we find functions $W^{(r)}_{1,2}(x)>0$ satisfying $\\int_{0}^{\\infty}x^{n}W^{(r)}_{1,2}(x)dx = {\\rho}_{1,2}^{(r)}(n)$. It is shown using criteria for uniqueness and non-uniqueness (Carleman, Krein, Berg, Pakes, Stoyanov) that for $r>1$ both ${\\rho}_{1,2}^{(r)}(n)$ give rise to non-unique solutions. Examples of such solutions are constructed using the technique of the inverse Mellin tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4846","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}