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作者:

Li, Yun-Zhang (Li, Yun-Zhang.) (学者:李云章) | Xue, Yan-Qin (Xue, Yan-Qin.)

收录:

Scopus SCIE

摘要:

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.

关键词:

Multiplier Parseval frame wavelet Wavelet

作者机构:

  • [ 1 ] [Li, Yun-Zhang]Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China
  • [ 2 ] [Xue, Yan-Qin]Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China

通讯作者信息:

  • 李云章

    [Li, Yun-Zhang]Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China

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来源 :

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS

ISSN: 1069-5869

年份: 2013

期: 5

卷: 19

页码: 1060-1077

1 . 2 0 0

JCR@2022

ESI学科: MATHEMATICS;

ESI高被引阀值:64

JCR分区:2

中科院分区:2

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