{"paper":{"title":"$G$-type Spaces of Ultradistributions over $\\mathbb{R}^d_+$ and the Weyl Pseudo-differential Operators with Radial Symbols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bojan Prangoski, Smiljana Jaksi\\'c, Stevan Pilipovi\\'c","submitted_at":"2016-02-12T11:23:14Z","abstract_excerpt":"The first part of the paper is devoted to the $G$-type spaces i.e. the spaces $G^\\alpha_\\alpha (\\mathbb R^d_+)$, $\\alpha\\geq 1$ and their duals which can be described as analogous to the Gelfand-Shilov spaces and their duals but with completely new justification of obtained results. The Laguerre type expansions of the elements in $G^\\alpha_\\alpha(\\mathbb R^d_+)$, $\\alpha\\geq 1$ and their duals characterise these spaces through the exponential and sub-exponential growth of coefficients. We provide the full topological description and by the nuclearity of $G_\\alpha^\\alpha(\\mathbb{R}^d_+)$, $\\alp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04017","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"}