The wavelet dimension function for real dilations and dilations admitting non-MSF wavelets
نویسندگان
چکیده
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 admitting non-MSF wavelets are characterized, and an example of a wavelet with respect to a non-expansive matrix is given. §
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