{"paper":{"title":"On a family of differential operators with the coupling parameter in the boundary condition","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"G. Rozenblum, M. Solomyak","submitted_at":"2005-10-18T09:18:15Z","abstract_excerpt":"We study a family of differential operators $L_\\alpha$ in two variables, depending on the coupling parameter $\\alpha\\ge0$ that appears only in the boundary conditions. Our main concern is the spectral properties of $L_\\alpha$, which turn out to be quite different for $\\alpha\\le 1$ and for $\\alpha>1$. In particular,\n $L_\\alpha$ has a unique self-adjoint realization for $\\alpha\\le 1$ and many such realizations for $\\alpha>1$. In the more difficult case $\\alpha>1$ an analysis of non-elliptic pseudodifferential operators in dimension one is involved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510371","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"}