160	1994	Johan Walden	johan@tdb.uu.se	Spectral Analysis of the Differentiation Operator in Wavelet Bases

			Abstract

We analyse how to use wavelets for solving hyperbolic partial
differential equations. The approach is to use wavelets to get a
sparse representation of the solution of the problem. The problem
is studied on a periodic domain, with periodized wavelets.
The order conditions for the differential operator d/dx in wavelet
space are analysed. An algorithm for finding the eigenvalue 
function of the differential operator is presented, and general 
conditions that ensure a "nicely behaving" eigenvalue function 
are derived.