L2(Rs)中正交尺度函数和正交小波的Fourier变换紧支集的刻画

Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (4): 1104-1118.

• Articles • Previous Articles Next Articles

The Characterization of Compact Support of Fourier Transform for Scaling Function and Orthonormal Wavelets of L²(R^s)

(Institute of Information and System Science, North University for Nationalities, Ningxia Yinchuan 750021), (Faculty of Science, Xi'an Jiaotong University, Xi'an 710049)|(School of Mathematics and Computer, Ningxia University, Ningxia, Yinchuan 750021)

Received:2007-07-01 Revised:2008-11-19 Online:2009-08-25 Published:2009-08-25
Supported by:
宁夏自然科学基金(NZ0846)、教育部科学技术研究重点项目(207124)、宁夏高等学校科学技术研究项目(2007JY007)和北方民族大学科学研究项目(2007Y043)资助

Abstract

Abstract:

In this paper, under a weaker condition, the authors give the sufficient and necessary condition that φ(x) is a scaling function of L²(R^s), in view of support of Fourier transform for φ(x). Furthermore, suppose {Ψ_μ} is an orthonormal wavelet of L²(R^s) and the whole support of its Fourier transform is
∪_μ supp{ψ_μ} = ∏^s_i₌₁[A_i, D_i] - ∏^s_i₌₁(B_i, C_i), A_i ≤ B_i ≤ C_i ≤ D_i, i =1, 2, … , s.
Under the weakest condition that each |ψ_μ|is continuous for ω ∈ ∂(∏^s_i₌₁[A_i, D_i]), the authors give results of the above whole support of {ψ_μ}, these results are characterized by some equalities and inequalities. They have improved completely Long's results and Zhang's results.

Key words: Orthonormal wavelets, Multiresolution analysis, Scaling function;Compact support, Fourier transform

CLC Number:

42C40

HUANG Yong-Dong, CHENG Zheng-Xing, HAN Hui-Li. The Characterization of Compact Support of Fourier Transform for Scaling Function and Orthonormal Wavelets of L²(R^s)[J].Acta mathematica scientia,Series A, 2009, 29(4): 1104-1118.

Trendmd

[1]	Qu Feifei, Deng Guantie. A Sharper Uncertainty Principle for L²(Rⁿ) Space [J]. Acta mathematica scientia,Series A, 2018, 38(4): 631-640.
[2]	LIU Feng, WU Huo-Xiong, ZHANG Dai-Qing. Parametric Marcinkiewicz Integrals with Rough Kernels Supported by Compound Subvarieties [J]. Acta mathematica scientia,Series A, 2014, 34(4): 1026-1039.
[3]	JIANG Pan-Pan, WANG Ze-Jun. Decay Estimates of Solutions for the p-System withGeneral Linear Dissipation [J]. Acta mathematica scientia,Series A, 2014, 34(4): 802-815.
[4]	XIE Xian-Hua, XIAO Xin-Yuan, XU Shao-Yuan, MA Li. L^p Boundedness of Multiple Marcinkiewicz Integral Operators with Rough Kernels [J]. Acta mathematica scientia,Series A, 2012, 32(5): 914-927.
[5]	JIN Shou-Bo, CHEN Pan-Feng, SUN Shan-Hui. Regularity of the Solution to the Dissipative Linear Boltzmann Equation [J]. Acta mathematica scientia,Series A, 2011, 31(6): 1662-1668.
[6]	XU Guan-Lei, WANG Xiao-Tong, XU Xiao-Gang. 2D Hilbert Transform and Bedrosian’s Principle Associated with Fractional Fourier Transform [J]. Acta mathematica scientia,Series A, 2011, 31(3): 814-828.
[7]	CHEN Dong-Xiang, LU Shan-Zhen. L^p Boundedness of \|Parabolic Littlewood-Paley Operator with Rough Kernel Belonging to F_α(Sⁿ^-1) [J]. Acta mathematica scientia,Series A, 2011, 31(2): 343-350.
[8]	CHENG Mei-Fang, ZHANG Zhen-Qiu. Average Decay Estimates for Fourier Transforms of Measure Supported on Homogeneous Hypersurfaces [J]. Acta mathematica scientia,Series A, 2011, 31(1): 76-81.
[9]	Huang Yongdong; Cheng Zhengxing. Explicit Construction of Wavelet Tight Frames with Dilation factor α [J]. Acta mathematica scientia,Series A, 2007, 27(1): 7-018.
[10]	CUI Li-Hong, CHENG Zheng-Xin, YANG Shou-Zhi. Explicit Structuer of Wavelet Tight Frames [J]. Acta mathematica scientia,Series A, 2004, 24(1): 94-104.
[11]	Feng Zhigang, Chen Gang. Nonorthogonal Wavelet Packets of Multiplicity r [J]. Acta mathematica scientia,Series A, 1998, 18(3): 277-283.
[12]	Shu Lisheng. The Spherical Functions and Fourier Transform on SL(2, R) [J]. Acta mathematica scientia,Series A, 1997, 17(2): 184-191.

The Characterization of Compact Support of Fourier Transform for Scaling Function and Orthonormal Wavelets of L²(R^s)

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 12

Metrics

Comments

Recommended 0

The Characterization of Compact Support of Fourier Transform for Scaling Function and Orthonormal Wavelets of L2(Rs)

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 12

Metrics

Comments

Recommended 0

The Characterization of Compact Support of Fourier Transform for Scaling Function and Orthonormal Wavelets of L²(R^s)