Non-MSF wavelets for the Hardy space H²()

الأصل · EN

We prove three results on wavelets for the Hardy space H²(). All wavelets constructed so far for H²() are MSF wavelets. We construct a family of H²-wavelets which are not MSF. An equivalence relation on H²-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H²-wavelets with Fourier transform discontinuous at the origin.