Non-msf Wavelets for the Hardy Space H(r)
نویسنده
چکیده
We prove three results on wavelets for the Hardy space H (R). All wavelets constructed so far for H(R) are MSF wavelets. We construct a family of H-wavelets which are not MSF. An equivalence relation on H-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H-wavelets with Fourier transform discontinuous at the origin.
منابع مشابه
Large classes of minimally supported frequency wavelets of L 2 ( R ) and H 2 ( R )
We introduce a method to construct large classes of MSF wavelets of the Hardy space H2(R) and symmetric MSF wavelets of L2(R), and discuss the classification of such sets. As application, we show that there are uncountably many wavelet sets of L2(R) and H2(R). We also enumerate all symmetric wavelets of L2(R) with at most three intervals in the positive axis as well as 3-interval wavelet sets o...
متن کامل$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework
In the present work the space $L_{p;r} $ which is continuously embedded into $L_{p} $ is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...
متن کاملNon-MSF a-Wavelets from a-Wavelet Sets
Generalizing the result of Bownik and Speegle [Approximation Theory X: Wavelets, Splines and Applications, Vanderbilt University Press, pp. 63–85, 2002], we provide plenty of non-MSF A-wavelets with the help of a given A-wavelet set. Further, by showing that the dimension function of the non-MSF A-wavelet constructed through an A-wavelet set W coincides with the dimension function of W , we con...
متن کاملConstruction of Non-msf Wavelets from Two-interval and Three-interval Wavelet Sets
In this paper, we construct non-MSF wavelets in L2(R) from twointerval and three-interval wavelet sets. AMS Subject Classification: 42C15, 42C40
متن کاملThe wavelet dimension function for real dilations and dilations admitting non-MSF wavelets
The wavelet dimension function for arbitrary real dilations is defined and used to address several questions involving the existence of MRA wavelets and well-localized wavelets for irrational dilations. The theory of quasi-affine frames for rational dilations and the existence of non-MSF wavelets for certain irrational dilations play an important role in this development. Expansive dilations ad...
متن کامل