{"paper":{"title":"Reconsideration of the multivariate moment problem and a new method for approximating multivariate integrals","license":"","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.FA","authors_text":"Hermann Render, Ognyan Kounchev","submitted_at":"2005-09-16T14:59:49Z","abstract_excerpt":"Due to its intimate relation to Spectral Theory and Schr\\\"{o}dinger operators, the multivariate moment problem has been a subject of many researches, so far without essential success (if one compares with the one--dimensional case). In the present paper we reconsider a basic axiom of the standard approach - the positivity of the measure. We introduce the so--called pseudopositive measures instead. One of our main achievements is the solution of the moment problem in the class of the pseudopositive measures. A measure \\ $\\mu$ is called pseudopositive if its Laplace-Fourier coefficients $\\mu_{k,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509380","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0509380/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}