{"paper":{"title":"The principal transmission condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Gerd Grubb","submitted_at":"2021-04-12T15:54:37Z","abstract_excerpt":"The paper treats pseudodifferential operators $P=Op(p(\\xi ))$ with homogeneous complex symbol $p(\\xi )$ of order $2a>0$, generalizing the fractional Laplacian $(-\\Delta )^a$ but lacking its symmetries, and taken to act on the halfspace $R^n_+$. The operators are seen to satisfy a principal $\\mu $-transmission condition relative to $R^n_+$, but generally not the full $\\mu $-transmission condition satisfied by $(-\\Delta )^a$ and related operators (with $\\mu =a$). However, $P$ acts well on the so-called $\\mu $-transmission spaces over $R^n_+$ (defined in earlier works), and when $P$ moreover is s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.05581","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.05581/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}