{"paper":{"title":"Higher Order Eigenvalues for Non-Local Schr\\\"odinger Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Feng-Yu Wang, Niels Jacob","submitted_at":"2017-03-29T09:52:57Z","abstract_excerpt":"Two-sided estimates for higher order eigenvalues are presented for a class of non-local Schr\\\"odinger operators by using the jump rate and the growth of the potential. For instance, let $L$ be the generator of a L\\'evy process with L\\'evy measure $\\nu(d z):= \\rho(z) d z$ such that $\\rho(z)=\\rho(-z)$ and $$c_1 |z|^{-(d+\\alpha_1)}\\le \\rho(z)\\le c_2|z|^{-(d+\\alpha_2)},\\ \\ |z|\\le \\kappa $$ for some constants $\\kappa, c_1,c_2>0$ and $\\alpha_1,\\alpha_2\\in (0,2),$ and let $c_3|x|^{\\theta_1} \\le V(x)\\le c_4|x|^{\\theta_2}$ for some constants $\\theta_1,\\theta_2, c_3,c_4>0$ and large $|x|$. Then the eige"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09954","kind":"arxiv","version":3},"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"}