{"paper":{"title":"Some remarks on boundary operators of Bessel extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.AP","authors_text":"Daniel Spector, Jesse Goodman","submitted_at":"2017-06-22T05:24:09Z","abstract_excerpt":"In this paper we study some boundary operators of a class of Bessel-type Littlewood-Paley extensions whose prototype is \\[\\Delta_x u(x,y) +\\frac{1-2s}{y} \\frac{\\partial u}{\\partial y}(x,y)+\\frac{\\partial^2 u}{\\partial y^2}(x,y)=0 \\text{ for }x\\in\\mathbb{R}^d, y>0, \\\\ u(x,0)=f(x) \\text{ for }x\\in\\mathbb{R}^d. \\] In particular, we show that with a logarithmic scaling one can capture the failure of analyticity of these extensions in the limiting cases $s=k \\in \\mathbb{N}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07169","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"}