Title:
Spectral Synthesis and $H^1(R)$
Abstract:
I will discuss joint work with C. R. Warner. We study spectral synthesis
using an integral considered by Beurling and Pollard,
\[ B(f,E) = \int_{E^c} \frac{|\hat{f}(t)|}{\rho(t,E)} dt,\] but on real $H^1(R)$. We introduce a class of sets, which can be controlled using $L^1(R)$ when they are large, but which seem to require $H^1(R)$ when the sets are small, such as points. |