Abstract
The problem to be discussed in this talk originated in an ongoing joint
research by Stefania Tracogna, Bruno Welfert and the speaker.
The latter research, which has a bearing on the famous Kreiss matrix
theorem, has led quite unexpectedly to a nontrivial problem concerning
Fourier series.
It is well known that Fourier approximation of order n is stable in
L_2, in that the effect on the approximations of any errors in the data
can be bounded suitably in terms of the L_2-norm of the errors. It
is a nontrivial question whether Fourier approximation is still
stable when errors are measured in a weighted L_2-norm
(instead of the standard L_2-norm). This is the question to be
adressed in this talk.
