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Full-Text Articles in Physical Sciences and Mathematics
Local Behavior Of Distributions And Applications, Jasson Vindas
Local Behavior Of Distributions And Applications, Jasson Vindas
LSU Doctoral Dissertations
This dissertation studies local and asymptotic properties of distributions (generalized functions) in connection to several problems in harmonic analysis, approximation theory, classical real and complex function theory, tauberian theory, summability of divergent series and integrals, and number theory. In Chapter 2 we give two new proofs of the Prime Number Theory based on ideas from asymptotic analysis on spaces of distributions. Several inverse problems in Fourier analysis and summability theory are studied in detail. Chapter 3 provides a complete characterization of point values of tempered distributions and functions in terms of a generalized pointwise Fourier inversion formula. The relation of …
Function Spaces, Wavelets And Representation Theory, Jens Gerlach Christensen
Function Spaces, Wavelets And Representation Theory, Jens Gerlach Christensen
LSU Doctoral Dissertations
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 …