Title: What are Rademacher functions?
Speaker: Maxwell Budd (Ohio State University)
Abstract: The binary expansion of a given number is normally stored as a sequence of zeros and ones. However, the Rademacher functions {$r_k(t)$} map the k-th binary digit of a number from 1 to -1 and from 0 to 1, resulting in a surprisingly useful construction. The functions form an incomplete orthonormal basis on [0,1] from which a complete basis, the Walsh system, can be constructed, and they also are a valuable instrument of proof. In this talk we will get an intuition for the Rademacher functions, use them to prove a classical formula, and explore their relations to probability theory and convergence.
Seminar URL: https://math.osu.edu/whatis
