{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-1631"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-1631","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"Vague convergence of spectral shift functions for periodic restrictions of one-dimensional Schrodinger operators","abstract":"We prove weak and vague convergence results for spectral shift functions associated with self-adjoint one-dimensional Schr\\\"odinger operators on intervals of the form $(-\\ell,\\ell)$ with periodic boundary conditions to the full-line spectral shift function in the infinite volume limit $\\ell\\to \\infty$. The approach employed relies on the use of a Krein-type resolvent identity to relate the resolvent of the operator with periodic boundary conditions to the corresponding operator with Dirichlet boundary conditions in combination with various operator theoretic facts.","abstract_html":"We prove weak and vague convergence results for spectral shift functions associated with self-adjoint one-dimensional Schr\\"odinger operators on intervals of the form $(-\\ell,\\ell)$ with periodic boundary conditions to the full-line spectral shift function in the infinite volume limit $\\ell\\to \\infty$. The approach employed relies on the use of a Krein-type resolvent identity to relate the resolvent of the operator with periodic boundary conditions to the corresponding operator with Dirichlet boundary conditions in combination with various operator theoretic facts.","abstract_has_math":true,"creators":["Murphy, John B."],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Nichols, Roger","Barioli, Francesco; van der Merwe, Lucas; Wang, Jin","College of Arts and Sciences"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T05:46:28Z","subjects":["Schrödinger operator","Operator theory"],"languages":["English","eng"],"rights":[],"rights_urls":["https://rightsstatements.org/page/InC/1.0/?language=en"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/486","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Nichols, Roger","Barioli, Francesco; van der Merwe, Lucas; Wang, Jin","College of Arts and Sciences"]},{"key":"dc:creator","label":"Author","values":["Murphy, John B."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016-12-01T08:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"]},{"key":"dc:relation","label":"Dc Relation","values":["Masters Theses and Doctoral Dissertations"]},{"key":"dc:type","label":"Dc Type","values":["Masters theses","Text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Schrödinger operator","Operator theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://rightsstatements.org/page/InC/1.0/?language=en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholar.utc.edu/theses/486"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Dept. of Mathematics","M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science."]},{"key":"dc:description.abstract","label":"Abstract","values":["We prove weak and vague convergence results for spectral shift functions associated with self-adjoint one-dimensional Schr\\\"odinger operators on intervals of the form $(-\\ell,\\ell)$ with periodic boundary conditions to the full-line spectral shift function in the infinite volume limit $\\ell\\to \\infty$. The approach employed relies on the use of a Krein-type resolvent identity to relate the resolvent of the operator with periodic boundary conditions to the corresponding operator with Dirichlet boundary conditions in combination with various operator theoretic facts."]},{"key":"dc:title","label":"Title","values":["Vague convergence of spectral shift functions for periodic restrictions of one-dimensional Schrodinger operators"]}]}],"canonical_facts":{"dc:contributor":["Nichols, Roger","Barioli, Francesco; van der Merwe, Lucas; Wang, Jin","College of Arts and Sciences"],"dc:creator":["Murphy, John B."],"dc:date":["2016-12-01T08:00:00Z"],"dc:description":["Dept. of Mathematics","M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science."],"dc:description.abstract":["We prove weak and vague convergence results for spectral shift functions associated with self-adjoint one-dimensional Schr\\\"odinger operators on intervals of the form $(-\\ell,\\ell)$ with periodic boundary conditions to the full-line spectral shift function in the infinite volume limit $\\ell\\to \\infty$. The approach employed relies on the use of a Krein-type resolvent identity to relate the resolvent of the operator with periodic boundary conditions to the corresponding operator with Dirichlet boundary conditions in combination with various operator theoretic facts."],"dc:identifier":["https://scholar.utc.edu/theses/486"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["https://rightsstatements.org/page/InC/1.0/?language=en"],"dc:subject":["Schrödinger operator","Operator theory"],"dc:title":["Vague convergence of spectral shift functions for periodic restrictions of one-dimensional Schrodinger operators"],"dc:type":["Masters theses","Text"]},"updated_at":"2026-07-24T05:46:28Z"}