| Date: | Mon, 12 Apr 1999 |
| From: | Peter Sheridan Dodds |
| Subject: | Ranting and Raving |
Richard Stone's
lawyers have approved the
following for release
to the media and the public:
Title: Fourier Series and Divergent Series
Spabstract: Numerous methods have been introduced over the last few
hundred years for attaching sums to divergent series. We'll begin by
quickly mentioning two of these, due to Cesaro and Borel, and describing
an extension of them using eigenvalues and eigenfunctions of operators.
The main part of the talk will then discuss how these relate to
convergence of Fourier series. We'll describe a famous theorem of Fejer
that shows that the convergence behaviour of Fourier series is much better
when we use Cesaro summation than just ordinary summation. But we'll then
outline a computation suggesting that in some ways Borel summation may be
even better.