## 談話会　Projections in the L1-algebra of a locally compact group

2010年 　 10月 27日 10時 15分 ～ 2010年 　 10月 27日 11時 15分

Keith F. Taylor (Dalhousie University)

If $G$ is a locally compact group, then the Banach space of
complex-valued functions which are integrable with respect to
left Haar measure is denoted $L^1(G)$. Equipped with convolution as
product, $L^1(G)$ is a Banach algebra. A function $f\in L^1(G)$ is called
a projection if $f*f = f$ (we also require $f$ to be self-adjoint).
We will show how to construct projections when $G=\R^m H$,
the semi-direct of Euclidean space with a closed subspace $H$
of $GL_m(\R)$.
We will also show how this construction leads to the discovery of
multi-dimensional wavelet-like transforms.