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Abstract:
Let A be a dxd expansive matrix with |detA|=2. An A-wavelet is a function such that is an orthonormal basis for . A measurable function f is called an A-wavelet multiplier if the inverse Fourier transform of is an A-wavelet whenever psi is an A-wavelet, where denotes the Fourier transform of psi. A-scaling function multiplier, A-PFW multiplier, semi-orthogonal A-PFW multiplier, MRA A-wavelet multiplier, MRA A-PFW multiplier and semi-orthogonal MRA A-PFW multiplier are defined similarly. In this paper, we prove that the above seven classes of multipliers are equivalent, and obtain a characterization of them. We then prove that if the set of all A-wavelet multipliers acts on some A-scaling function (A-wavelet, A-PFW, semi-orthogonal A-PFW, MRA A-wavelet, MRA A-PFW, semi-orthogonal MRA A-PFW), the orbit is arcwise connected in , and that if the generator of an orbit is an MRA A-PFW, the orbit is equal to the set of all MRA A-PFWs whose Fourier transforms have same module, and is also equal to the set of all MRA A-PFWs with corresponding pseudo-scaling functions having the same module of their Fourier transforms.
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JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
ISSN: 1069-5869
Year: 2013
Issue: 5
Volume: 19
Page: 1060-1077
1 . 2 0 0
JCR@2022
ESI Discipline: MATHEMATICS;
JCR Journal Grade:2
CAS Journal Grade:2
Cited Count:
WoS CC Cited Count: 1
SCOPUS Cited Count: 1
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 3
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