{"paper":{"title":"Anisotropic Shubin operators and eigenfunctions expansions in Gelfand-Shilov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Luigi Rodino, Marco Cappiello, Stevan Pilipovic, Todor Gramchev","submitted_at":"2016-09-20T15:13:16Z","abstract_excerpt":"We derive new results on the characterization of Gelfand--Shilov spaces $\\mathcal{S}^\\mu_\\nu (\\R^n)$, $\\mu,\\nu >0$, $\\mu+\\nu \\geq 1$ by Gevrey estimates of the $L^2$ norms of iterates of $(m,k)$ anisotropic globally elliptic Shubin (or $\\Gamma$) type operators, $(-\\Delta)^{m/2} +| x |^k$ with $m,k\\in 2\\N$ being a model operator, and on the decay of the Fourier coefficients in the related eigenfunction expansions. Similar results are obtained for the spaces $\\Sigma^\\mu_\\nu (\\R^n)$, $\\mu,\\nu >0$, $\\mu+\\nu > 1$, cf. \\eqref{GSdef}. In contrast to the symmetric case $\\mu = \\nu$ and $k=m$ (classical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06214","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"}