Date

2016

Document Type

Dissertation

Degree

Doctor of Philosophy

Department

Mathematics

First Adviser

Neel, Robert W.

Other advisers/committee members

Napier, Terry; Conus, Daniel; Shank, Nathan

Abstract

A multiresolution analysis is a tool used in the construction of orthogonal wavelets. The dilation equation is an equation that arises naturally when using an MRA to construct a wavelet basis. One way to understand the dilation equation, and its solution, the scaling function, is through a measure theoretic approach. By constructing a solution to the signed measure dilation equation, we give a new way of approximating the scaling function by dyadic step functions. We also give a method of controlling the support in the two-dimensional case.

Included in

Mathematics Commons

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