{"id":{"repo_id":"missouri","oai_identifier":"oai:mospace.umsystem.edu:10355/5566"},"canonical_url":"https://search.dev.ndltd.org/etd/missouri/oai:mospace.umsystem.edu:10355/5566","repository":{"repo_id":"missouri","name":"University of Missouri","base_url":"https://mospace.umsystem.edu/oai/request"},"display":{"title":"Box approximation and related techniques in spectral theory","abstract":"This dissertation is concerned with various aspects of the spectral theory of differential and pseudodifferential operators. It consists of two chapters. The first chapter presents a study of a family of spectral shift functions [xi]r, each associated with a pair of self-adjoint Schrödinger operators on a finite interval (0, r). Specifically, we investigate the limit behavior of the functions [xi]r when the parameter r approaches infinity. We prove that an ergodic limit of [xi]r coincides with the spectral shift function associated with the singular problem on the semi-infinite interval. In the second chapter, we study the attractor of the dynamical system r [arrow] Ar, where Ar is the truncated Wiener-Hopf operator surrounded by operators of multiplication by the function e[superscript alpha/2] [absolute value of dot], [alpha][greater than] 0. We show that in the case when the symbol of the Wiener-Hopf operator is a rational function with two real zeros the dynamical system r [arrow] Ar possesses a nontrivial attractor of a limit-circle type.","abstract_html":"This dissertation is concerned with various aspects of the spectral theory of differential and pseudodifferential operators. It consists of two chapters. The first chapter presents a study of a family of spectral shift functions [xi]r, each associated with a pair of self-adjoint Schrödinger operators on a finite interval (0, r). Specifically, we investigate the limit behavior of the functions [xi]r when the parameter r approaches infinity. We prove that an ergodic limit of [xi]r coincides with the spectral shift function associated with the singular problem on the semi-infinite interval. In the second chapter, we study the attractor of the dynamical system r [arrow] Ar, where Ar is the truncated Wiener-Hopf operator surrounded by operators of multiplication by the function e[superscript alpha/2] [absolute value of dot], [alpha][greater than] 0. We show that in the case when the symbol of the Wiener-Hopf operator is a rational function with two real zeros the dynamical system r [arrow] Ar possesses a nontrivial attractor of a limit-circle type.","abstract_has_math":false,"creators":["Borovyk, Vita, 1979-"],"institution":"University of Missouri--Columbia","degree_name":"Ph. 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D.) University of Missouri-Columbia 2008.","Dissertations, Academic -- University of Missouri--Columbia -- Mathematics."]},{"key":"dc:description.abstract","label":"Abstract","values":["This dissertation is concerned with various aspects of the spectral theory of differential and pseudodifferential operators. It consists of two chapters. The first chapter presents a study of a family of spectral shift functions [xi]r, each associated with a pair of self-adjoint Schrödinger operators on a finite interval (0, r). Specifically, we investigate the limit behavior of the functions [xi]r when the parameter r approaches infinity. We prove that an ergodic limit of [xi]r coincides with the spectral shift function associated with the singular problem on the semi-infinite interval. In the second chapter, we study the attractor of the dynamical system r [arrow] Ar, where Ar is the truncated Wiener-Hopf operator surrounded by operators of multiplication by the function e[superscript alpha/2] [absolute value of dot], [alpha][greater than] 0. We show that in the case when the symbol of the Wiener-Hopf operator is a rational function with two real zeros the dynamical system r [arrow] Ar possesses a nontrivial attractor of a limit-circle type."]},{"key":"dc:title","label":"Title","values":["Box approximation and related techniques in spectral theory"]}]}],"canonical_facts":{"dc:contributor.advisor":["Makarov, Konstantin A."],"dc:creator":["Borovyk, Vita, 1979-"],"dc:date.accessioned":["2010-02-23T16:34:04Z"],"dc:date.available":["2010-02-23T16:34:04Z"],"dc:date.issued":["2008"],"dc:description":["The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.","Title from title screen of research.pdf file (viewed on June 2, 2009)","Vita.","Includes bibliographical references.","Thesis (Ph. D.) 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In the second chapter, we study the attractor of the dynamical system r [arrow] Ar, where Ar is the truncated Wiener-Hopf operator surrounded by operators of multiplication by the function e[superscript alpha/2] [absolute value of dot], [alpha][greater than] 0. We show that in the case when the symbol of the Wiener-Hopf operator is a rational function with two real zeros the dynamical system r [arrow] Ar possesses a nontrivial attractor of a limit-circle type."],"dc:identifier.doi":["https://doi.org/10.32469/10355/5566"],"dc:identifier.uri":["https://hdl.handle.net/10355/5566"],"dc:language":["English"],"dc:language.iso":["eng"],"dc:publisher":["University of Missouri--Columbia"],"dc:rights":["OpenAccess."],"dc:title":["Box approximation and related techniques in spectral theory"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics (MU)"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph. 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