Session S13 - Harmonic Analysis, Fractal Geometry, and Applications

Friday, July 16, 15:30 ~ 16:00 UTC-3

Improving Estimates in Discrete Settings

Michael Lacey

Georgia Institute of Technology, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Averages improve smoothness and integrability of functions. This well known principle is very familiar in continuous settings. There is a wealth of results and approaches to questions of this type in a variety of continuous settings. The investigation of related questions in the discrete setting is much more recent. We will survey recent results in this area, outlining the types of results that are possible, some that have been established, and the range of techniques used. We will touch on averages over the integers, as well as finite field settings.

Joint work with Rui Han, Louisiana State University, Fan Yang, Australian National University, Hamed Mousavi, Georgia Tech, Christina Gianitsi, Georgia Tech and Jacob Rahami, Georgia Tech.

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