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 Advisor

Pereyra, Maria Cristina

First Committee Member (Chair)

Embid, Pedro

Second Committee Member

Skripka, Anna

Language

English

Keywords

Hilbert Transform, Dyadic Shift Operators, Random Dyadic Grids, Singular Integrals, Fourier Multipliers

Document Type

Thesis

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