Publication Date
1-28-2015
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.
Degree Name
Mathematics
Level of Degree
Masters
Department Name
Mathematics & Statistics
First Committee Member (Chair)
Maria Cristina Pereyra
Second Committee Member
Pedro Embid
Third Committee Member
Anna Skripka
Language
English
Keywords
Hilbert Transform, Dyadic Shift Operators, Random Dyadic Grids, Singular Integrals, Fourier Multipliers
Document Type
Thesis
Recommended Citation
Atasever, Nuriye. "The Hilbert Transform as an Average of Dyadic Shift Operators." (2015). https://digitalrepository.unm.edu/math_etds/3
