I give an overview of the basic theory of Hilbert spaces necessary to understand the convergence of the Fourier series for square integrable functions. I state the necessary theorems and definitions to understand the formulations of the problem in a Hilbert space framework, and then I give some applications of the theory along the way.
","abstract_html":"<p>I give an overview of the basic theory of Hilbert spaces necessary to understand the convergence of the Fourier series for square integrable functions. I state the necessary theorems and definitions to understand the formulations of the problem in a Hilbert space framework, and then I give some applications of the theory along the way.</p>","abstract_has_math":false,"creators":["Harris, Terri Joan, Mrs."],"institution":null,"degree_name":"Master of Arts in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Ventura, Belisario"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-01T07:00:00Z","date_published":"2015-09-01T07:00:00Z","updated_at":"2026-07-24T01:52:53Z","subjects":["Uniform convergence","trigonometric system","orthogonal","orthonormal","Gram-Schmidt","Analysis","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.lib.csusb.edu/etd/244","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ventura, Belisario"]},{"key":"dc:creator","label":"Author","values":["Harris, Terri Joan, Mrs."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-08-18T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Uniform convergence","trigonometric system","orthogonal","orthonormal","Gram-Schmidt","Analysis","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.lib.csusb.edu/etd/244"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["I give an overview of the basic theory of Hilbert spaces necessary to understand the convergence of the Fourier series for square integrable functions. I state the necessary theorems and definitions to understand the formulations of the problem in a Hilbert space framework, and then I give some applications of the theory along the way.
"]},{"key":"dc:title","label":"Title","values":["HILBERT SPACES AND FOURIER SERIES"]}]}],"canonical_facts":{"dc:contributor":["Ventura, Belisario"],"dc:creator":["Harris, Terri Joan, Mrs."],"dc:date.available":["2015-08-18T07:00:00Z"],"dc:description.abstract":["I give an overview of the basic theory of Hilbert spaces necessary to understand the convergence of the Fourier series for square integrable functions. I state the necessary theorems and definitions to understand the formulations of the problem in a Hilbert space framework, and then I give some applications of the theory along the way.
"],"dc:identifier":["https://scholarworks.lib.csusb.edu/etd/244"],"dc:subject":["Uniform convergence","trigonometric system","orthogonal","orthonormal","Gram-Schmidt","Analysis","Mathematics"],"dc:title":["HILBERT SPACES AND FOURIER SERIES"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Arts in Mathematics"]},"updated_at":"2026-07-24T01:52:53Z"}