{"id":{"repo_id":"unm","oai_identifier":"oai:digitalrepository.unm.edu:math_etds-1002"},"canonical_url":"https://search.dev.ndltd.org/etd/unm/oai:digitalrepository.unm.edu:math_etds-1002","repository":{"repo_id":"unm","name":"University of New Mexico","base_url":"https://digitalrepository.unm.edu/do/oai/"},"display":{"title":"The Hilbert Transform as an Average of Dyadic Shift Operators","abstract":"In this thesis we discuss Petermichls characterization of the Hilbert transform as an average of dyadic shift operators following the presentation by Thomas Hytonen [Hyt]. A linear and bounded operator T in L2(R) that commutes with translations, dilations and anticommutes with reflections must be a constant multiple of Hilbert transform; T = cH. Using this principle Stefanie Petermichl showed that we can write H as a suitable average of dyadic operators [Pet]. Each Dyadic Shift Operator does not have the symmetries that characterize the Hilbert transform, but an average over all random dyadic grids do.","abstract_html":"In this thesis we discuss Petermichls characterization of the Hilbert transform as an average of dyadic shift operators following the presentation by Thomas Hytonen [Hyt]. A linear and bounded operator T in L2(R) that commutes with translations, dilations and anticommutes with reflections must be a constant multiple of Hilbert transform; T = cH. Using this principle Stefanie Petermichl showed that we can write H as a suitable average of dyadic operators [Pet]. Each Dyadic Shift Operator does not have the symmetries that characterize the Hilbert transform, but an average over all random dyadic grids do.","abstract_has_math":false,"creators":["Atasever, Nuriye"],"institution":null,"degree_name":"Mathematics","degree_level":"Masters","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Pereyra, Maria Cristina","Maria Cristina Pereyra","Pedro Embid","Anna Skripka"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-28T08:00:00Z","date_published":"2015-01-28T08:00:00Z","updated_at":"2026-07-24T05:27:37Z","subjects":["Hilbert Transform","Dyadic Shift Operators","Random Dyadic Grids","Singular Integrals","Fourier Multipliers"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalrepository.unm.edu/math_etds/3"],"render_values":[{"text":"https://digitalrepository.unm.edu/math_etds/3","href":"https://digitalrepository.unm.edu/math_etds/3","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1928/25730","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Pereyra, Maria Cristina","Maria Cristina Pereyra","Pedro Embid","Anna Skripka"]},{"key":"dc:creator","label":"Author","values":["Atasever, Nuriye"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters","Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Hilbert Transform","Dyadic Shift Operators","Random Dyadic Grids","Singular Integrals","Fourier Multipliers"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/1928/25730","https://digitalrepository.unm.edu/math_etds/3"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we discuss Petermichls characterization of the Hilbert transform as an average of dyadic shift operators following the presentation by Thomas Hytonen [Hyt]. A linear and bounded operator T in L2(R) that commutes with translations, dilations and anticommutes with reflections must be a constant multiple of Hilbert transform; T = cH. Using this principle Stefanie Petermichl showed that we can write H as a suitable average of dyadic operators [Pet]. Each Dyadic Shift Operator does not have the symmetries that characterize the Hilbert transform, but an average over all random dyadic grids do."]},{"key":"dc:title","label":"Title","values":["The Hilbert Transform as an Average of Dyadic Shift Operators"]}]}],"canonical_facts":{"dc:contributor":["Pereyra, Maria Cristina","Maria Cristina Pereyra","Pedro Embid","Anna Skripka"],"dc:creator":["Atasever, Nuriye"],"dc:description.abstract":["In this thesis we discuss Petermichls characterization of the Hilbert transform as an average of dyadic shift operators following the presentation by Thomas Hytonen [Hyt]. A linear and bounded operator T in L2(R) that commutes with translations, dilations and anticommutes with reflections must be a constant multiple of Hilbert transform; T = cH. Using this principle Stefanie Petermichl showed that we can write H as a suitable average of dyadic operators [Pet]. Each Dyadic Shift Operator does not have the symmetries that characterize the Hilbert transform, but an average over all random dyadic grids do."],"dc:identifier":["http://hdl.handle.net/1928/25730","https://digitalrepository.unm.edu/math_etds/3"],"dc:language":["English"],"dc:subject":["Hilbert Transform","Dyadic Shift Operators","Random Dyadic Grids","Singular Integrals","Fourier Multipliers"],"dc:title":["The Hilbert Transform as an Average of Dyadic Shift Operators"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Masters","Thesis"],"thesis:degree_name":["Mathematics"]},"updated_at":"2026-07-24T05:27:37Z"}