The pointwise Holder spectrum of self-affine functions

Date: 
2019/05/24 Fri 14:00 - 15:00
Room: 
Room 609, Building No.6
Speaker: 
Pieter Allaart
Affiliation: 
University of North Texus
Abstract: 

We study general self-affine functions on an interval, which include the Takagi function and Okamoto's functions. We show that the pointwise Holder spectrum of these functions can be completely determined. In most cases, the Holder spectrum is given by the multifractal formalism, but there is an important class of exceptions. In fact, it is possible to give exact (but complicated) expressions for the pointwise Holder exponent of any self-affine function at any point. The proofs of these results use a variety of techniques: Divided differenes, constrained optimization, and general Hausdorff measure estimates. This is joint work with S. Dubuc.