Jocelyn Quaintance

Hilbert Spaces, Hilbert Bases, and Fourier Series

Date: 11/14/2018
Time: 4:00PM-5:00PM
Place: 315 Armstrong Hall

Abstract: In honor of Salah Hamad's dissertation defense, I will give a graduate student accessible
talk discussing the basic theory of Hilbert spaces. In particular, I will define what it means for a Hilbert space
$E$ to have a Hilbert basis $(u_k)_{k\in K}$ and show how the concept of a Hilbert basis provides the canonical representation
of $E$ in terms of $l^2(K)$, namely the famous Riesz-Fischer theorem. Then I will discuss the connection between Hilbert bases and
the Fourier series of a square period function, ending with a brief recap of Joseph Fourier's fascinating life.

Date, Location:
2018-11-14