Degree Type

Dissertation

Date of Award

2004

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Fritz Keinert

Abstract

We review the one-dimensional setting of wavelet theory and generalize it to nonseparable multivariate wavelets. This process presents significant technical difficulties. Some techniques of the one-dimensional setting carry over in a more or less straightforward way; some do not generalize at all.;The main results include the following: an algorithm for computing the moments for multivariate multiwavelets; a necessary and sufficient condition for the approximation order; the lifting scheme for multivariate wavelets; and a generalization of the method of Lai [12] for the biorthogonal completion of a polyphase matrix under suitable conditions.;One-dimensional techniques which cannot be generalized include the factorization of the polyphase matrix, and a general solution to the completion problem.

DOI

https://doi.org/10.31274/rtd-180813-27

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu

Copyright Owner

Ghan Shyam Bhatt

Language

en

Proquest ID

AAI3158317

File Format

application/pdf

File Size

76 pages

Included in

Mathematics Commons

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