{"id":{"repo_id":"unm","oai_identifier":"oai:digitalrepository.unm.edu:math_etds-1022"},"canonical_url":"https://search.dev.ndltd.org/etd/unm/oai:digitalrepository.unm.edu:math_etds-1022","repository":{"repo_id":"unm","name":"University of New Mexico","base_url":"https://digitalrepository.unm.edu/do/oai/"},"display":{"title":"Jost Functions for Jacobi Operators with Super-exponentially Decaying Parameters","abstract":"The decay of the parameters for a Jacobi operator is related to the analyticity of the Jost function associated with J, which is in turn related to the spectral measure of J. Damanik and Simon demonstrated the equivalence between the exponential decay of these parameters and the analyticity of the Jost function on a disk whose radius is given by the rate of decay. In this paper, these equivalences are summarized, and an additional equivalence is shown in the case when the parameters decay super-exponentially. In this case, the Jost function will be an entire function with finite growth order no greater than twice the inverse of the decay rate.","abstract_html":"The decay of the parameters for a Jacobi operator is related to the analyticity of the Jost function associated with J, which is in turn related to the spectral measure of J. Damanik and Simon demonstrated the equivalence between the exponential decay of these parameters and the analyticity of the Jost function on a disk whose radius is given by the rate of decay. In this paper, these equivalences are summarized, and an additional equivalence is shown in the case when the parameters decay super-exponentially. In this case, the Jost function will be an entire function with finite growth order no greater than twice the inverse of the decay rate.","abstract_has_math":false,"creators":["Kaul, Fred, II"],"institution":null,"degree_name":"Mathematics","degree_level":"Masters","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Zinchenko, Maxim","Maxim Zinchenko","Anna Skripka","Maria Cristina Pereyra"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-08-25T07:00:00Z","date_published":"2016-08-25T07:00:00Z","updated_at":"2026-07-24T05:27:37Z","subjects":["spectral theory","jacobi operator","jost function","hilbert space"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalrepository.unm.edu/math_etds/23"],"render_values":[{"text":"https://digitalrepository.unm.edu/math_etds/23","href":"https://digitalrepository.unm.edu/math_etds/23","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1928/32959","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Zinchenko, Maxim","Maxim Zinchenko","Anna Skripka","Maria Cristina Pereyra"]},{"key":"dc:creator","label":"Author","values":["Kaul, Fred, II"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters","Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["spectral theory","jacobi operator","jost function","hilbert space"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/1928/32959","https://digitalrepository.unm.edu/math_etds/23"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The decay of the parameters for a Jacobi operator is related to the analyticity of the Jost function associated with J, which is in turn related to the spectral measure of J. Damanik and Simon demonstrated the equivalence between the exponential decay of these parameters and the analyticity of the Jost function on a disk whose radius is given by the rate of decay. In this paper, these equivalences are summarized, and an additional equivalence is shown in the case when the parameters decay super-exponentially. In this case, the Jost function will be an entire function with finite growth order no greater than twice the inverse of the decay rate."]},{"key":"dc:title","label":"Title","values":["Jost Functions for Jacobi Operators with Super-exponentially Decaying Parameters"]}]}],"canonical_facts":{"dc:contributor":["Zinchenko, Maxim","Maxim Zinchenko","Anna Skripka","Maria Cristina Pereyra"],"dc:creator":["Kaul, Fred, II"],"dc:description.abstract":["The decay of the parameters for a Jacobi operator is related to the analyticity of the Jost function associated with J, which is in turn related to the spectral measure of J. Damanik and Simon demonstrated the equivalence between the exponential decay of these parameters and the analyticity of the Jost function on a disk whose radius is given by the rate of decay. In this paper, these equivalences are summarized, and an additional equivalence is shown in the case when the parameters decay super-exponentially. In this case, the Jost function will be an entire function with finite growth order no greater than twice the inverse of the decay rate."],"dc:identifier":["http://hdl.handle.net/1928/32959","https://digitalrepository.unm.edu/math_etds/23"],"dc:language":["English"],"dc:subject":["spectral theory","jacobi operator","jost function","hilbert space"],"dc:title":["Jost Functions for Jacobi Operators with Super-exponentially Decaying Parameters"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Masters","Thesis"],"thesis:degree_name":["Mathematics"]},"updated_at":"2026-07-24T05:27:37Z"}