{"paper":{"title":"Boundary values of holomorphic functions and heat kernel method in translation-invariant distribution spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Jasson Vindas, Pavel Dimovski, Stevan Pilipovic","submitted_at":"2014-08-31T09:10:50Z","abstract_excerpt":"We study boundary values of holomorphic functions in translation-invariant distribution spaces of type $\\mathcal{D}'_{E'_{\\ast}}$. New edge of the wedge theorems are obtained. The results are then applied to represent $\\mathcal{D}'_{E'_{\\ast}}$ as a quotient space of holomorphic functions. We also give representations of elements of $\\mathcal{D}'_{E'_{\\ast}}$ via the heat kernel method. Our results cover as particular instances the cases of boundary values, analytic representations, and heat kernel representations in the context of the Schwartz spaces $\\mathcal{D}'_{L^{p}}$, $\\mathcal{B}'$, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0197","kind":"arxiv","version":2},"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"}