{"paper":{"title":"On the spectral theory of one functional-difference operator from conformal field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.CA","math.MP"],"primary_cat":"math.SP","authors_text":"Leon A. Takhtajan, Ludwig D. Faddeev","submitted_at":"2014-08-01T21:19:31Z","abstract_excerpt":"In the paper we consider a functional-difference operator $H=U+U^{-1}+V$, where $U$ and $V$ are self-adjoint Weyl operators satisfying $UV=q^{2}VU$ with $q=e^{\\pi i\\tau}$ and $\\tau>0$. The operator $H$ has applications in the conformal field theory and in the representation theory of quantum groups. Using modular quantum dilogarithm - a $q$-deformation of the Euler's dilogarithm - we define the scattering solution and the Jost solutions, derive an explicit formula for the resolvent of the self-adjoint operator $H$ in the Hilbert space $L^{2}(\\mathbb{R})$, and prove the eigenfunction expansion "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0307","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"}