{"paper":{"title":"Distributions associated to homogeneous distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A.V.Kosyak (Institute of Mathematics, Civil Engineering University), Kiev), V.I.Polischook (St. Petersburg State Polytechnical University), V.M.Shelkovich (St.-Petersburg State Architecture","submitted_at":"2012-05-03T08:48:44Z","abstract_excerpt":"In this paper we continue to study {\\it quasi associated homogeneous distributions \\rm{(}generalized functions\\rm{)}} which were introduced in the paper by V.M. Shelkovich, Associated and quasi associated homogeneous distributions (generalized functions), J. Math. An. Appl., {\\bf 338}, (2008), 48-70. [arXiv:math/0608669]. For the multidimensional case we give the characterization of these distributions in the terms of the dilatation operator $U_{a}$ (defined as $U_{a}f(x)=f(ax)$, $x\\in \\bR^n$, $a >0$) and its generator $\\sum_{j=1}^{n}x_j\\frac{\\partial}{\\partial x_j}$. It is proved that $f_k\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0650","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"}