{"id":{"repo_id":"mississippi","oai_identifier":"oai:egrove.olemiss.edu:etd-1678"},"canonical_url":"https://search.dev.ndltd.org/etd/mississippi/oai:egrove.olemiss.edu:etd-1678","repository":{"repo_id":"mississippi","name":"University of Mississippi","base_url":"https://egrove.olemiss.edu/do/oai/"},"display":{"title":"Orthogonal Polynomials On An Arc Of The Unit Circle With Respect To A Generalized Jacobi Weight: A Riemann-Hilbert Method Approach","abstract":"We investigate the asymptotic behavior of polynomials orthogonal over a symmetric arc of the unit circle with respect to a generalized Jacobi-type weight. Full asymptotic expansions for the orthogonal polynomials are obtained at every point of the complex plane. Our method of proof is based on a characterization of the orthogonal polynomials as solutions of a 2X2 matrix Riemann-Hilbert problem, which extends to the unit circle the original Riemann-Hilbert characterization for orthogonal polynomials on the real line, first discovered by Fokas, Its, and Kitaev. In order to extricate the behavior of the polynomials from its Riemann-Hilbert matrix representation, we follow the steepest descent method of matrix transformations developed by Deift and Zhou.","abstract_html":"We investigate the asymptotic behavior of polynomials orthogonal over a symmetric arc of the unit circle with respect to a generalized Jacobi-type weight. Full asymptotic expansions for the orthogonal polynomials are obtained at every point of the complex plane. Our method of proof is based on a characterization of the orthogonal polynomials as solutions of a 2X2 matrix Riemann-Hilbert problem, which extends to the unit circle the original Riemann-Hilbert characterization for orthogonal polynomials on the real line, first discovered by Fokas, Its, and Kitaev. In order to extricate the behavior of the polynomials from its Riemann-Hilbert matrix representation, we follow the steepest descent method of matrix transformations developed by Deift and Zhou.","abstract_has_math":false,"creators":["Naugle, Lynsey Cargile"],"institution":null,"degree_name":"Ph.D. in Mathematics","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Erwin Mina Diaz","Cecille Labuda","Qingying Bu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-01-01T08:00:00Z","date_published":"2017-01-01T08:00:00Z","updated_at":"2026-07-24T03:05:53Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://egrove.olemiss.edu/etd/679","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Erwin Mina Diaz","Cecille Labuda","Qingying Bu"]},{"key":"dc:creator","label":"Author","values":["Naugle, Lynsey Cargile"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-06-20T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D. in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://egrove.olemiss.edu/etd/679"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We investigate the asymptotic behavior of polynomials orthogonal over a symmetric arc of the unit circle with respect to a generalized Jacobi-type weight. Full asymptotic expansions for the orthogonal polynomials are obtained at every point of the complex plane. Our method of proof is based on a characterization of the orthogonal polynomials as solutions of a 2X2 matrix Riemann-Hilbert problem, which extends to the unit circle the original Riemann-Hilbert characterization for orthogonal polynomials on the real line, first discovered by Fokas, Its, and Kitaev. In order to extricate the behavior of the polynomials from its Riemann-Hilbert matrix representation, we follow the steepest descent method of matrix transformations developed by Deift and Zhou."]},{"key":"dc:title","label":"Title","values":["Orthogonal Polynomials On An Arc Of The Unit Circle With Respect To A Generalized Jacobi Weight: A Riemann-Hilbert Method Approach"]}]}],"canonical_facts":{"dc:contributor":["Erwin Mina Diaz","Cecille Labuda","Qingying Bu"],"dc:creator":["Naugle, Lynsey Cargile"],"dc:date.available":["2019-06-20T07:00:00Z"],"dc:description.abstract":["We investigate the asymptotic behavior of polynomials orthogonal over a symmetric arc of the unit circle with respect to a generalized Jacobi-type weight. Full asymptotic expansions for the orthogonal polynomials are obtained at every point of the complex plane. Our method of proof is based on a characterization of the orthogonal polynomials as solutions of a 2X2 matrix Riemann-Hilbert problem, which extends to the unit circle the original Riemann-Hilbert characterization for orthogonal polynomials on the real line, first discovered by Fokas, Its, and Kitaev. In order to extricate the behavior of the polynomials from its Riemann-Hilbert matrix representation, we follow the steepest descent method of matrix transformations developed by Deift and Zhou."],"dc:identifier":["https://egrove.olemiss.edu/etd/679"],"dc:subject":["Mathematics"],"dc:title":["Orthogonal Polynomials On An Arc Of The Unit Circle With Respect To A Generalized Jacobi Weight: A Riemann-Hilbert Method Approach"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D. in Mathematics"]},"updated_at":"2026-07-24T03:05:53Z"}