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2 Bulletin of the Polish Academy of Sciences. Mathematics

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Non-MSF wavelets for the Hardy space H^2(R)

Behera B.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 2

169-178

All wavelets constructed so far for the Hardy space H^2(R) are MSF wavelets. We construct a family of H^2-wavelets which are not MSF. An equivalence relation on H^2-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H^2-wavelets with Fourier transform not vanishing in any neighbourhood of the origin.

Some new examples of wavelets in the Hardy space [H^2](R)

Majchrowska G.

Bulletin of the Polish Academy of Sciences. Mathematics

2001

Vol. 49, no 2

141-149

In this paper we get some new examples of wavelet sets and scaling sets in [H^2](R). In particular we prove that there exists a wavelet which does not belong to any [L^p](R) for p < 2.