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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Fetbrandt, Joshua Taylor, "Hölder Extensions for Non-Standard Fractal Koch Curves" (2014). Theses and Dissertations. 4097.
fractal, koch curve, extension