Doctor of Philosophy (PhD)
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.
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Christensen, Jens Gerlach, "Function Spaces, Wavelets and Representation Theory" (2009). LSU Doctoral Dissertations. 2241.