| Abstract: | A wavelet multiplier is a function whose product with the Fourier transform of a wavelet is the Fourier transform of a wavelet.
We characterize the wavelet multipliers, as well as the scaling function multipliers and low pass filter multipliers. We then
prove that if the set of all wavelet multipliers acts on the set of all MRA wavelets, the orbits are the sets of all MRA wavelets
whose Fourier transforms have equal absolute values, and these are also equal to the sets, of all MRA wavelets with the corresponding
scaling functions having the same absolute values of their Fourier transforms. As an application of these techniques, we prove
that the set of MRA wavelets is arcwise connected in L2(R).
Dedicated to Eugene Fabes
The Wutam Consortium |
