{"paper":{"title":"Spectral Properties of Harmonic Toeplitz Operators and Applications to the Perturbed Krein Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Georgi Raikov, Vincent Bruneau","submitted_at":"2016-09-27T00:32:46Z","abstract_excerpt":"We consider harmonic Toeplitz operators $T_V = PV:{\\mathcal H}(\\Omega) \\to {\\mathcal H}(\\Omega)$ where $P: L^2(\\Omega) \\to {\\mathcal H}(\\Omega)$ is the orthogonal projection onto ${\\mathcal H}(\\Omega) = \\left\\{u \\in L^2(\\Omega)\\,|\\,\\Delta u = 0 \\; \\mbox{in}\\;\\Omega\\right\\}$, $\\Omega \\subset {\\mathbb R}^d$, $d \\geq 2$, is a bounded domain with $\\partial \\Omega \\in C^\\infty$, and $V: \\Omega \\to {\\mathbb C}$ is a suitable multiplier. First, we complement the known criteria which guarantee that $T_V$ is in the $p$th Schatten-von Neumann class $S_p$, by sufficient conditions which imply $T_V \\in S_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08229","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":""},"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"}