Session S13 - Harmonic Analysis, Fractal Geometry, and Applications

Friday, July 16, 14:55 ~ 15:25 UTC-3

Adjacent Dyadic Systems

Theresa Anderson

Purdue University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

A very useful tool in analysis and applications, called by many names, is the "1/3" trick, which says that any ball in Euclidean space is contained in a dyadic cube of roughly the same size, where the dyadic cube comes from one of a finite number of dyadic grids. For $\mathbb{R}^d$, Conde showed that the optimal number of grids to perform this trick is $d+1$. In recent joint work, we completely classify all grids that allow this property, termed "adjacent dyadic systems", and discuss an interesting connection to number theory that arises.

Joint work with Bingyang Hu (Purdue University, USA).

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