{"paper":{"title":"Generalized localization for spherical partial sums of multiple Fourier series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ravshan Ashurov","submitted_at":"2019-01-10T06:19:14Z","abstract_excerpt":"In this paper the generalized localization principle for the spherical partial sums of the multiple Fourier series in the $L_2$ - class is proved, that is, if $f\\in L_2(T^N)$ and $f=0$ on an open set $\\Omega \\subset T^N$, then it is shown that the spherical partial sums of this function converge to zero almost - everywhere on $\\Omega$. It has been previously known that the generalized localization is not valid in $L_p(T^N)$ when $1\\leq p<2$. Thus the problem of generalized localization for the spherical partial sums is completely solved in $L_p(T^N)$, $p\\geq 1$: if $p\\geq2$ then we have the ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03028","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"}