Title page for ETD etd-07092009-141954


Type of Document Dissertation
Author Christensen, Jens Gerlach
Author's Email Address vepjan@math.lsu.edu
URN etd-07092009-141954
Title Function Spaces, Wavelets and Representation Theory
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Gestur Olafsson Committee Chair
Boris Rubin Committee Member
Mark Davidson Committee Member
Oliver Dasbach Committee Member
William Adkins Committee Member
Wei-Hsung Wang Dean's Representative
Keywords
  • Wavelets
  • coorbit spaces
  • light cone
Date of Defense 2009-06-26
Availability unrestricted
Abstract
This dissertation is concerned with the interplay between the theory of Banach spaces and representations of groups. The wavelet transform has proven to be a useful tool in characterizing and constructing Banach spaces, and we investigate a generalization of an already known technique due to H.G. Feichtinger and K. Gröchenig. This generalization is presented in Chapter 3, and in Chapters 4 and 5 we present examples of spaces which can be described using the theory. The first example clears up a question regarding a wavelet characterization of Bergman spaces related to a non-integrable representation. The second example is a wavelet characterization of Besov spaces on the forward light cone.
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