Good and Bad Functions for Translates

Andy Parrish (Eastern Illinois University)

14-May-2022, 18:00-19:00 (23 months ago)

Abstract: We say that a set of functions is good for a sequence of operators if the sequence converges for every function in the set; the set is bad if there is a function in the set for which the sequence of operators does not converge. For example, given a fixed sequence tending to zero, the continuous functions are pointwise good for translations by this sequence-- yet bounded Lebesgue-measurable functions are pointwise bad. We'll discuss how the set of functions that are pointwise good for translation by any sequence is precisely the set of functions locally equal a.e. to a Riemann-integrable function. Time permitting, we will also explore some new perspectives on a well-known conjecture due to Erdos. This is joint work with Joseph Rosenblatt (UIUC).

dynamical systems

Audience: researchers in the discipline


Little school dynamics

Series comments: Email dynamics@aimath.org to ask for the Zoom link.

Organizers: David Farmer*, Andy Parrish*
*contact for this listing

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