{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-2238"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-2238","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"On the parametrization of self-adjoint extensions of singular Sturm-Liouville operators","abstract":"The self-adjoint extensions of a lower semi-bounded minimal Sturm–Liouville operator are parametrized using generalized boundary values defined by fixed choices of special nonoscillatory solutions, called principal and nonprincipal solutions. However, principal and nonprincipal solutions are not unique, and different choices yield different generalized boundary values. Therefore, the parametrization of self-adjoint extensions inherently depends upon the choices of principal and nonprincipal solutions. Using known properties of principal and nonprincipal solutions, Wronskian techniques, and the Pl¨ucker identity, we find the relation between self-adjoint extensions for two different parametrizations.","abstract_html":"The self-adjoint extensions of a lower semi-bounded minimal Sturm–Liouville operator are parametrized using generalized boundary values defined by fixed choices of special nonoscillatory solutions, called principal and nonprincipal solutions. However, principal and nonprincipal solutions are not unique, and different choices yield different generalized boundary values. Therefore, the parametrization of self-adjoint extensions inherently depends upon the choices of principal and nonprincipal solutions. Using known properties of principal and nonprincipal solutions, Wronskian techniques, and the Pl¨ucker identity, we find the relation between self-adjoint extensions for two different parametrizations.","abstract_has_math":false,"creators":["Beckler, Caleb"],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Nichols, Roger","Kong, Lingju; Çetinkaya, Ayça; Wang, Xiunan","College of Arts and Sciences"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T05:47:28Z","subjects":["Operator theory","Selfadjoint operators","Spectral theory (Mathematics)","Sturm-Liouville equation"],"languages":["English","eng"],"rights":[],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/1056","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Nichols, Roger","Kong, Lingju; Çetinkaya, Ayça; Wang, Xiunan","College of Arts and Sciences"]},{"key":"dc:creator","label":"Author","values":["Beckler, Caleb"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2026-05-01T07:00:00Z"]},{"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":["Operator theory","Selfadjoint operators","Spectral theory (Mathematics)","Sturm-Liouville equation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholar.utc.edu/theses/1056"]}]},{"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":["The self-adjoint extensions of a lower semi-bounded minimal Sturm–Liouville operator are parametrized using generalized boundary values defined by fixed choices of special nonoscillatory solutions, called principal and nonprincipal solutions. However, principal and nonprincipal solutions are not unique, and different choices yield different generalized boundary values. Therefore, the parametrization of self-adjoint extensions inherently depends upon the choices of principal and nonprincipal solutions. Using known properties of principal and nonprincipal solutions, Wronskian techniques, and the Pl¨ucker identity, we find the relation between self-adjoint extensions for two different parametrizations."]},{"key":"dc:title","label":"Title","values":["On the parametrization of self-adjoint extensions of singular Sturm-Liouville operators"]}]}],"canonical_facts":{"dc:contributor":["Nichols, Roger","Kong, Lingju; Çetinkaya, Ayça; Wang, Xiunan","College of Arts and Sciences"],"dc:creator":["Beckler, Caleb"],"dc:date":["2026-05-01T07:00:00Z"],"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":["The self-adjoint extensions of a lower semi-bounded minimal Sturm–Liouville operator are parametrized using generalized boundary values defined by fixed choices of special nonoscillatory solutions, called principal and nonprincipal solutions. However, principal and nonprincipal solutions are not unique, and different choices yield different generalized boundary values. Therefore, the parametrization of self-adjoint extensions inherently depends upon the choices of principal and nonprincipal solutions. Using known properties of principal and nonprincipal solutions, Wronskian techniques, and the Pl¨ucker identity, we find the relation between self-adjoint extensions for two different parametrizations."],"dc:identifier":["https://scholar.utc.edu/theses/1056"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Operator theory","Selfadjoint operators","Spectral theory (Mathematics)","Sturm-Liouville equation"],"dc:title":["On the parametrization of self-adjoint extensions of singular Sturm-Liouville operators"],"dc:type":["Masters theses","Text"]},"updated_at":"2026-07-24T05:47:28Z"}