Thursday,
March 11, 1999, 12:15 p.m. in GWC Room 604
Gilbert G. Walter
Department of Mathematical Sciences, University of Wisconsin-Milwaukee
Wavelet solutions of first kind integral equations
Abstract
Most applications of orthogonal wavelets to integral equations have been
to second kind or to singular integral equations. The wavelets used are usually
spline based or Daubechies wavelets. But Meyer’s bandlimited wavelets have a
number of properties that make them useful even for first kind equations whose
solution is an ill-posed problem. This talk presents a method based on these wavelets that is suitable for convolution integral equations.
The rates of convergence based on certain smoothness hypotheses of the kernel are found.
A description
of the construction and of some properties of these Meyer wavelets will also be
included.
