{"paper":{"title":"Ultrarelativistic (Cauchy) spectral problem in the infinite well","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP","quant-ph"],"primary_cat":"math-ph","authors_text":"Elena V. Kirichenko, Mariusz \\.Zaba, Piotr Garbaczewski, Vladimir Stephanovich","submitted_at":"2015-05-06T08:16:59Z","abstract_excerpt":"We analyze spectral properties of the ultrarelativistic (Cauchy) operator $|\\Delta |^{1/2}$, provided its action is constrained exclusively to the interior of the interval $[-1,1] \\subset R$. To this end both analytic and numerical methods are employed. New high-accuracy spectral data are obtained. A direct analytic proof is given that trigonometric functions $\\cos(n\\pi x/2)$ and $\\sin(n\\pi x)$, for integer $n$ are {\\it not} the eigenfunctions of $|\\Delta |_D^{1/2}$, $D=(-1,1)$. This clearly demonstrates that the traditional Fourier multiplier representation of $|\\Delta |^{1/2}$ becomes defect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01277","kind":"arxiv","version":2},"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"}