Title: Perturbed Brascamp-Lieb inequalities and application to Parsell-Vinogradov systems Authors: Zhang, Ruixiang Advisors: Sarnak, Peter C Contributors: Mathematics Department Keywords: Brascamp-Lieb inequalityDecouplingParsell-Vinogradov systemPolynomial 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. URI: http://arks.princeton.edu/ark:/88435/dsp0137720g37s Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: catalog.princeton.edu Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Mathematics
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8327871561050415, "perplexity": 5172.650391398824}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232255092.55/warc/CC-MAIN-20190519181530-20190519203530-00196.warc.gz"}