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Decoupling and Restriction Inequalities for Smooth Compact Surfaces in Three Dimensions.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Decoupling and Restriction Inequalities for Smooth Compact Surfaces in Three Dimensions./
Author:	Li, Jianhui.
Description:	1 online resource (78 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
Contained By:	Dissertations Abstracts International84-11B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30492469click for full text (PQDT)
ISBN:	9798379520878

Decoupling and Restriction Inequalities for Smooth Compact Surfaces in Three Dimensions.
Li, Jianhui.

Decoupling and Restriction Inequalities for Smooth Compact Surfaces in Three Dimensions. - 1 online resource (78 pages)

Source: Dissertations Abstracts International, Volume: 84-11, Section: B.

Thesis (Ph.D.)--The University of Wisconsin - Madison, 2023.

Includes bibliographical references

This dissertation establishes general decoupling and restriction inequalities for smooth compact surfaces in R3. First, we prove decoupling inequalities in R3 for the graphs of all bivariate polynomials of degree at most k with bounded coefficients over a compact set, with the decoupling constant uniform in the coefficients of those polynomials. As a consequence, we prove a decoupling inequality for smooth compact surfaces in R3 . This extends the decoupling theorem of Bourgain and Demeter to all smooth surfaces. Second, we prove sharp L2 Fourier restriction inequalities for smooth compact surfaces in R3 equipped with the affine surface measure or a power thereof. The estimates are uniform for all surfaces defined by the graph of polynomials of degrees at most k with bounded coefficients. The primary tool is a variant of the aforementioned decoupling inequalities for these surfaces.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798379520878Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Restriction inequalitiesIndex Terms--Genre/Form:

542853
Electronic books.

Decoupling and Restriction Inequalities for Smooth Compact Surfaces in Three Dimensions.
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245 1 0 $a Decoupling and Restriction Inequalities for Smooth Compact Surfaces in Three Dimensions.
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300 $a 1 online resource (78 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
500 $a Advisor: Stovall, Betsy.
502 $a Thesis (Ph.D.)--The University of Wisconsin - Madison, 2023.
504 $a Includes bibliographical references
520 $a This dissertation establishes general decoupling and restriction inequalities for smooth compact surfaces in R3. First, we prove decoupling inequalities in R3 for the graphs of all bivariate polynomials of degree at most k with bounded coefficients over a compact set, with the decoupling constant uniform in the coefficients of those polynomials. As a consequence, we prove a decoupling inequality for smooth compact surfaces in R3 . This extends the decoupling theorem of Bourgain and Demeter to all smooth surfaces. Second, we prove sharp L2 Fourier restriction inequalities for smooth compact surfaces in R3 equipped with the affine surface measure or a power thereof. The estimates are uniform for all surfaces defined by the graph of polynomials of degrees at most k with bounded coefficients. The primary tool is a variant of the aforementioned decoupling inequalities for these surfaces.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
653 $a Restriction inequalities
653 $a Three dimensions
653 $a Smooth compact surfaces
653 $a Decoupling
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a The University of Wisconsin - Madison. $b Mathematics. $3 2101076
773 0 $t Dissertations Abstracts International $g 84-11B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30492469 $z click for full text (PQDT)