Final Examination of

Eric Olson

for the

Degree of Doctor of Philosophy in Mathematics

Wednesday, 25 August 1999, 2:15pm

Rawles Hall 316

Dissertation: The Orthogonal Projection of Fractal Sets

The research in my Ph.D. thesis focuses on the problem of embedding a fractal subset of a Hilbert space into a finite dimensional space by means of an orthogonal projection. We first consider subsets with finite fractal dimension and then study what happens in the case of finite Bouligand dimension. Our aim is to obtain more stringent regularity properties for the inverse of the embedding map.

Revised Fri Aug 28 10:57:04 PDT 1999