{"paper":{"title":"The Borel transform and linear nonlocal equations: applications to zeta-nonlocal field models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alan Ch\\'avez, Enr\\'ique G. Reyes, Humberto Prado","submitted_at":"2019-07-04T23:14:23Z","abstract_excerpt":"We define rigorously operators of the form $f(\\partial_t)$, in which $f$ is an analytic function on a simply connected domain. Our formalism is based on the Borel transform on entire functions of exponential type. We study existence and regularity of real-valued solutions for the nonlocal in time equation \\begin{equation*} f(\\partial_t) \\phi = J(t) \\; \\; , \\quad t\\in \\mathbb{R}\\; , \\end{equation*}. and we find its more general solution as a restriction to $\\mathbb{R}$ of an entire function of exponential type.\n  As an important special case, we solve explicitly the linear nonlocal zeta field e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02617","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"}