#### Abstract

Let K be a non-standard fractal Koch curve with contraction factor α. Assume α is of the form α = 2+1/m for some m ∈ N and that K is embedded in a larger domain Ω. Further suppose that u is any Hölder continuous function on K. Then for each such m ∈ N and iteration n ≥ 0, we construct a bounded linear operator Πn which extends u from the prefractal Koch curve Kn into the whole of Ω. Unfortunately, our sequence of extension functions Πnu are not bounded in norm in the limit because the upper bound is a strictly increasing function of n; this prevents us from demonstrating uniform convergence in the limit.

#### Degree

MS

#### College and Department

Physical and Mathematical Sciences; Mathematics

#### Rights

http://lib.byu.edu/about/copyright/

#### BYU ScholarsArchive Citation

Fetbrandt, Joshua Taylor, "Hölder Extensions for Non-Standard Fractal Koch Curves" (2014). *All Theses and Dissertations*. 4097.

http://scholarsarchive.byu.edu/etd/4097

#### Date Submitted

2014-06-11

#### Document Type

Thesis

#### Handle

http://hdl.lib.byu.edu/1877/etd7015

#### Keywords

fractal, koch curve, extension