{"paper":{"title":"On A Finite Range Decomposition of the Resolvent of a Fractional Power of the Laplacian II. The Torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"P. K. Mitter","submitted_at":"2017-01-15T21:03:37Z","abstract_excerpt":"In previous papers, [M1, M2], [M3], we proved the existence as well as regularity of a finite range decomposition for the resolvent $G_{\\alpha} (x-y,m^2) = ((-\\Delta)^{\\alpha\\over 2} + m^{2})^{-1} (x-y) $, for $0<\\alpha <2$ and all real $m$, in the lattice ${\\bf Z}^{d}$ for dimension $d\\ge 2$. In this paper, which is a continuation of the previous one, we extend those results by proving the existence as well as regularity of a finite range decomposition for the same resolvent but now on the lattice torus ${\\bf Z}^{d}/L^{N+1}{\\bf Z}^{d} $ for $d\\ge 2$ provided $m\\neq 0$ and $0<\\alpha <2$. We al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04111","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"}