{"id":{"repo_id":"missouri","oai_identifier":"oai:mospace.umsystem.edu:10355/62261"},"canonical_url":"https://search.dev.ndltd.org/etd/missouri/oai:mospace.umsystem.edu:10355/62261","repository":{"repo_id":"missouri","name":"University of Missouri","base_url":"https://mospace.umsystem.edu/oai/request"},"display":{"title":"Topics in spectral theory of differential operators /","abstract":"This dissertation is devoted to two eigenvalue counting problems: Determining the asymptotic behavior of large eigenvalues of self-adjoint extensions of partial differential operators, and computing the number of negative eigenvalues for bounded from below operators with compact resolvents. In the first part of this thesis we derive a Weyl-type asymptotic formula and a bound for the eigenvalue counting function for the Krein-von Neumann extension of differential operators on open bounded subsets of R n. In the second part of this thesis we obtain a formula relating the Maslov index, a topological invariant counting the signed number of conjugate points of paths of Lagrangian planes in H1/2 ([boundary symbol]) x H-1/2 ([boundary symbol]) and the Morse index, the number of negative eigenvalues, for the second order differential operators with domains of definition contained in H1 ([omega]) for open bounded subsets [omega] [symbol] R[subscript n].","abstract_html":"This dissertation is devoted to two eigenvalue counting problems: Determining the asymptotic behavior of large eigenvalues of self-adjoint extensions of partial differential operators, and computing the number of negative eigenvalues for bounded from below operators with compact resolvents. In the first part of this thesis we derive a Weyl-type asymptotic formula and a bound for the eigenvalue counting function for the Krein-von Neumann extension of differential operators on open bounded subsets of R n. In the second part of this thesis we obtain a formula relating the Maslov index, a topological invariant counting the signed number of conjugate points of paths of Lagrangian planes in H1/2 ([boundary symbol]) x H-1/2 ([boundary symbol]) and the Morse index, the number of negative eigenvalues, for the second order differential operators with domains of definition contained in H1 ([omega]) for open bounded subsets [omega] [symbol] R[subscript n].","abstract_has_math":false,"creators":["Sukhtaiev, Selim, 1990-"],"institution":"University of Missouri--Columbia","degree_name":"Ph. D.","degree_level":"Doctoral","degree_discipline":"Mathematics (MU)","degree_department":null,"school":null,"contributors":[],"advisors":["Gesztesy, Fritz, 1953-","Latushkin, Yuri, 1956-"],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-24T03:09:16Z","subjects":[],"languages":["eng","English"],"rights":["OpenAccess."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10355/62261","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Gesztesy, Fritz, 1953-","Latushkin, Yuri, 1956-"]},{"key":"dc:creator","label":"Author","values":["Sukhtaiev, Selim, 1990-"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-12-18T15:10:51Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-12-18T15:10:51Z"]},{"key":"dc:date.issued","label":"Date","values":["2017"]},{"key":"dc:publisher","label":"Institution","values":["University of Missouri--Columbia"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics (MU)"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Missouri--Columbia"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["OpenAccess."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10355/62261"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This dissertation is devoted to two eigenvalue counting problems: Determining the asymptotic behavior of large eigenvalues of self-adjoint extensions of partial differential operators, and computing the number of negative eigenvalues for bounded from below operators with compact resolvents. In the first part of this thesis we derive a Weyl-type asymptotic formula and a bound for the eigenvalue counting function for the Krein-von Neumann extension of differential operators on open bounded subsets of R n. In the second part of this thesis we obtain a formula relating the Maslov index, a topological invariant counting the signed number of conjugate points of paths of Lagrangian planes in H1/2 ([boundary symbol]) x H-1/2 ([boundary symbol]) and the Morse index, the number of negative eigenvalues, for the second order differential operators with domains of definition contained in H1 ([omega]) for open bounded subsets [omega] [symbol] R[subscript n]."]},{"key":"dc:title","label":"Title","values":["Topics in spectral theory of differential operators /"]}]}],"canonical_facts":{"dc:contributor.advisor":["Gesztesy, Fritz, 1953-","Latushkin, Yuri, 1956-"],"dc:creator":["Sukhtaiev, Selim, 1990-"],"dc:date.accessioned":["2017-12-18T15:10:51Z"],"dc:date.available":["2017-12-18T15:10:51Z"],"dc:date.issued":["2017"],"dc:description.abstract":["This dissertation is devoted to two eigenvalue counting problems: Determining the asymptotic behavior of large eigenvalues of self-adjoint extensions of partial differential operators, and computing the number of negative eigenvalues for bounded from below operators with compact resolvents. In the first part of this thesis we derive a Weyl-type asymptotic formula and a bound for the eigenvalue counting function for the Krein-von Neumann extension of differential operators on open bounded subsets of R n. In the second part of this thesis we obtain a formula relating the Maslov index, a topological invariant counting the signed number of conjugate points of paths of Lagrangian planes in H1/2 ([boundary symbol]) x H-1/2 ([boundary symbol]) and the Morse index, the number of negative eigenvalues, for the second order differential operators with domains of definition contained in H1 ([omega]) for open bounded subsets [omega] [symbol] R[subscript n]."],"dc:identifier.uri":["https://hdl.handle.net/10355/62261"],"dc:language":["English"],"dc:language.iso":["eng"],"dc:publisher":["University of Missouri--Columbia"],"dc:rights":["OpenAccess."],"dc:title":["Topics in spectral theory of differential operators /"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics (MU)"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["University of Missouri--Columbia"]},"updated_at":"2026-07-24T03:09:16Z"}