On noncommutative lacunary multipliers.

Simple item page
dc.contributor.advisorMei, Tao, 1974-
dc.creatorLiu, Zhen-chuan, 1992-
dc.creator.orcid0000-0002-6092-5473
dc.date.accessioned2024-07-30T12:42:00Z
dc.date.available2024-07-30T12:42:00Z
dc.date.created2023-12
dc.date.issued2023-12
dc.date.submittedDecember 2023
dc.date.updated2024-07-30T12:42:09Z
dc.description.abstractThis thesis delves into the exploration of Paley’s inequality and the Marcinkiewicz multiplier theorem, focusing particularly on their applications to lacunary sequences within the framework of noncommutative harmonic analysis. Emphasis is placed on the “thin sets” in harmonic analysis, in particular on Λp-sets and their potential influence on the structures and properties of von Neumann algebras and Schatten p-classes. This work aims to establish a cohesive link between operator theory and Fourier analysis on discrete groups and Schatten p-classes. The first part discusses about Paley’s theory of lacunary Fourier series for von Neumann algebra of discrete groups. The results unify and generalize the work of Rudin for abelian discrete ordered groups and the work of Lust-Piquard and Pisier for operator valued functions, and provide new examples of Paley sets and Λ(p) sets on free groups. The second part focuses on the Marcinkiewicz type multiplier theory for the boundedness of Schur multipliers on the Schatten p-classes. This implies a new unconditional decomposition for the Schatten p-classes, 1 < p < ∞.
dc.format.mimetypeapplication/pdf
dc.identifier.uri
dc.identifier.urihttps://hdl.handle.net/2104/12856
dc.language.isoEnglish
dc.rights.accessrightsNo access – contact librarywebmaster@baylor.edu
dc.titleOn noncommutative lacunary multipliers.
dc.typeThesis
dc.type.materialtext
local.embargo.lift2025-12-01
local.embargo.terms2025-12-01
thesis.degree.departmentBaylor University. Dept. of Mathematics.
thesis.degree.grantorBaylor University
thesis.degree.namePh.D.
thesis.degree.programMathematics
thesis.degree.schoolBaylor University

Files

Original bundle

Now showing 1 - 3 of 3
No Thumbnail Available
Name:
LIU-PRIMARY-2023.pdf
Size:
378.44 KB
Format:
Adobe Portable Document Format
Download
No Thumbnail Available
Name:
1697133139433-LIU Full Copyright Request and Approval.pdf
Size:
539.61 KB
Format:
Adobe Portable Document Format
Download
No Thumbnail Available
Name:
1712861845840-Liu_RightsLink Printable License.pdf
Size:
95.72 KB
Format:
Adobe Portable Document Format
Download

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
38.47 KB
Format:
Plain Text
Description:
Download

Collections

Electronic Theses and Dissertations
Theses/Dissertations - Mathematics