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University of New Mexico
The Hilbert Transform as an Average of Dyadic Shift Operators
Abstract
dc:description.abstractIn 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.
Degree
thesis:*- Name thesis:degree_name
- Mathematics
- Level thesis:degree_level
- Masters
- Discipline thesis:degree_discipline
- Mathematics & Statistics
- Year
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Atasever, Nuriye
- Contributors dc:contributor
-
- Pereyra, Maria Cristina
- Maria Cristina Pereyra
- Pedro Embid
- Anna Skripka
Subjects
dc:subject × 5Rights
- Language dc:language
- English
Identifiers
dc:identifier.*- OAI identifier oai:identifier
- oai:digitalrepository.unm.edu:math_etds-1002