Analytical properties of real-valued functions through continuum trees

Sascha Troscheit (University of Vienna)

Thursday 28th July 15:00-16:00 Maths 311B

Abstract

In this talk we will explore analytical properties, such as Hölder continuity, of functions on [0,1] through the lens of continuum tree spaces. Surprisingly, analytical properties of the functions are linked with the dimension theoretic properties of this "dual" continuum tree space. These tree spaces originally came from probability theory and the study of Brownian motion. In this talk we will show that applying dimension theory to those dual spaces is the "right thing" to do. As an application we provide a concise proof of a theorem by Picard that links Hölder regularity with the upper box counting dimension of the tree, along with some new results.
Based on joint work with Maik Gröger.

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