{"paper":{"title":"Range-separated tensor representation of the discretized multidimensional Dirac delta and elliptic operator inverse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Boris N. Khoromskij","submitted_at":"2018-12-06T17:41:56Z","abstract_excerpt":"In this paper, we introduce the operator dependent range-separated tensor approximation of the discretized Dirac delta in $\\mathbb{R}^d$. It is constructed by application of the discrete elliptic operator to the range-separated decomposition of the associated Green kernel discretized on the Cartesian grid in $\\mathbb{R}^d$. The presented operator dependent local-global splitting of the Dirac delta can be applied for solving the potential equations in non-homogeneous media when the density in the right-hand side is given by the large sum of pointwise singular charges. We show how the idea of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02684","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"}