The Cayley-Hamilton Theorem is an important result in the study of linear transformations over finite dimensional vector spaces. In this thesis, we show that the Cayley-Hamilton Theorem can be extended to self-adjoint trace-class operators and to closed self-adjoint operators with trace-class resolvent over a separable Hilbert space. Applications of these results include calculating operators resolvents and finding the inverse of a frame operator.
","abstract_html":"<p>The Cayley-Hamilton Theorem is an important result in the study of linear transformations over finite dimensional vector spaces. In this thesis, we show that the Cayley-Hamilton Theorem can be extended to self-adjoint trace-class operators and to closed self-adjoint operators with trace-class resolvent over a separable Hilbert space. Applications of these results include calculating operators resolvents and finding the inverse of a frame operator.</p>","abstract_has_math":false,"creators":["Teguia, Alberto Mokak"],"institution":null,"degree_name":"MS (Master of Science)","degree_level":"Thesis - unrestricted","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2005,"date_issued":"2005-08-16T07:00:00Z","date_published":"2005-08-16T07:00:00Z","updated_at":"2026-07-24T02:19:43Z","subjects":["Meromorphic continuation","Inverse frame operator","Elliptic Operators","Cayley-Hamilton Theorem","Zeta function","Applied Mathematics","Physical Sciences and Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/1024","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Teguia, Alberto Mokak"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2005-08-16T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - unrestricted"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS (Master of Science)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Meromorphic continuation","Inverse frame operator","Elliptic Operators","Cayley-Hamilton Theorem","Zeta function","Applied Mathematics","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright by the authors."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dc.etsu.edu/context/etd/article/2181/viewcontent/TeguiaA052705f.pdf","https://dc.etsu.edu/etd/1024"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Cayley-Hamilton Theorem is an important result in the study of linear transformations over finite dimensional vector spaces. In this thesis, we show that the Cayley-Hamilton Theorem can be extended to self-adjoint trace-class operators and to closed self-adjoint operators with trace-class resolvent over a separable Hilbert space. Applications of these results include calculating operators resolvents and finding the inverse of a frame operator.
"]},{"key":"dc:title","label":"Title","values":["Extensions of the Cayley-Hamilton Theorem with Applications to Elliptic Operators and Frames."]}]}],"canonical_facts":{"dc:creator":["Teguia, Alberto Mokak"],"dc:date.issued":["2005-08-16T07:00:00Z"],"dc:description.abstract":["The Cayley-Hamilton Theorem is an important result in the study of linear transformations over finite dimensional vector spaces. In this thesis, we show that the Cayley-Hamilton Theorem can be extended to self-adjoint trace-class operators and to closed self-adjoint operators with trace-class resolvent over a separable Hilbert space. Applications of these results include calculating operators resolvents and finding the inverse of a frame operator.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/2181/viewcontent/TeguiaA052705f.pdf","https://dc.etsu.edu/etd/1024"],"dc:rights":["Copyright by the authors."],"dc:subject":["Meromorphic continuation","Inverse frame operator","Elliptic Operators","Cayley-Hamilton Theorem","Zeta function","Applied Mathematics","Physical Sciences and Mathematics"],"dc:title":["Extensions of the Cayley-Hamilton Theorem with Applications to Elliptic Operators and Frames."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:19:43Z"}