{"paper":{"title":"p-Adic Schr\\\"{o}dinger-Type Operator with Point Interactions","license":"","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"S. Albeverio, S. Kuzhel, S. Torba","submitted_at":"2007-03-27T14:58:41Z","abstract_excerpt":"A $p$-adic Schr\\\"{o}dinger-type operator $D^{\\alpha}+V_Y$ is studied. $D^{\\alpha}$ ($\\alpha>0$) is the operator of fractional differentiation and $V_Y=\\sum_{i,j=1}^nb_{ij}<\\delta_{x_j}, \\cdot>\\delta_{x_i}$ $(b_{ij}\\in\\mathbb{C})$ is a singular potential containing the Dirac delta functions $\\delta_{x}$ concentrated on points $\\{x_1,...,x_n\\}$ of the field of $p$-adic numbers $\\mathbb{Q}_p$. It is shown that such a problem is well-posed for $\\alpha>1/2$ and the singular perturbation $V_Y$ is form-bounded for $\\alpha>1$. In the latter case, the spectral analysis of $\\eta$-self-adjoint operator r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0703077","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"}