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UBC Theses and Dissertations
Configurations and decoupling : a few problems in Euclidean harmonic analysis Yang, Tongou
Abstract
In this thesis, we study two topics in Euclidean harmonic analysis. The first one is the configurations contained in fractal-like sets in the Euclidean space. The other is decoupling for various geometric objects in the Euclidean space. In the study of Euclidean configurations, we first discuss the background, address their subtleties and do a simple survey on this subject. Then we proceed to the proof of my main result, which demonstrates the topological property of a set containing a similar copy of sequences converging to zero. In the study of decoupling, we first formulate a general decoupling inequality and discuss some general upper and lower bound estimates Then we move on to decoupling for manifolds in Euclidean space, and in particular curves in the plane. We then state a classical result by Bourgain and Demeter and use it to prove a decoupling inequality that works uniformly for all polynomials up to a certain degree, generalising an earlier result of Biswas et al. in the plane.
Item Metadata
Title |
Configurations and decoupling : a few problems in Euclidean harmonic analysis
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2021
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Description |
In this thesis, we study two topics in Euclidean harmonic analysis. The
first one is the configurations contained in fractal-like sets in the Euclidean
space. The other is decoupling for various geometric objects in the Euclidean
space.
In the study of Euclidean configurations, we first discuss the background,
address their subtleties and do a simple survey on this subject. Then we
proceed to the proof of my main result, which demonstrates the topological
property of a set containing a similar copy of sequences converging to zero.
In the study of decoupling, we first formulate a general decoupling inequality and discuss some general upper and lower bound estimates Then
we move on to decoupling for manifolds in Euclidean space, and in particular curves in the plane. We then state a classical result by Bourgain and
Demeter and use it to prove a decoupling inequality that works uniformly
for all polynomials up to a certain degree, generalising an earlier result of
Biswas et al. in the plane.
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Genre | |
Type | |
Language |
eng
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Date Available |
2021-04-14
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0396689
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2021-05
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International