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Title: Perturbed Brascamp-Lieb inequalities and application to Parsell-Vinogradov systems
Authors: Zhang, Ruixiang
Advisors: Sarnak, Peter C
Contributors: Mathematics Department
Keywords: Brascamp-Lieb inequality
Parsell-Vinogradov system
Polynomial Method
Subjects: Mathematics
Issue Date: 2017
Publisher: Princeton, NJ : Princeton University
Abstract: In this thesis, we study the perturbed Brascamp-Lieb inequalities and its applications in translation-dilation systems. We prove the endpoint perturbed Brascamp-Lieb inequalities using polynomial partition techniques. We also look at the Parsell-Vinogradov system and verify the Brascamp-Lieb condition holds in its decoupling approach. As a corollary of this and the work of Guo, the main conjecture about the system is true in dimension $2$ and can be proved by the decoupling approach.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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