The Traits of Canonical Banach Frames Generated by Multiple Scaling Functions and Applications in Applied Materials

Jing Li Gao; Shi Hui Cheng

doi:10.4028/www.scientific.net/AMR.684.663

Paper Titles

Developing a Model for Risk and Responsibility Management Share Amongst Stakeholders Consortium in Construction Projects
p.639

Concepts of Risk in Construction Projects
p.644

FIR Digital Filter Design Based on Virtual Instrument
p.653

Building the Model of Near-Level Coal Deposit
p.657

The Traits of Canonical Banach Frames Generated by Multiple Scaling Functions and Applications in Applied Materials
p.663

Stagnant Nonuniform Acoustic Wave
p.667

Comparison of Three Short Term Wind Power Forecasting Methods
p.671

Probabilistic Reactive Power Optimization of Distribution Network Considering Stochastic Wind Speed and Load
p.676

An Overview of Osmotic Power: A Viable Power Generation Technology for Present and Future
p.680

HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 684The Traits of Canonical Banach Frames Generated by...

The Traits of Canonical Banach Frames Generated by Multiple Scaling Functions and Applications in Applied Materials

Abstract:

Frame theory has become a popular subject in scientific research during the past twenty years. In our study we use generalized multiresolution analyses in with dilation factor 4. We describe, in terms of the underlying multiresolution structure, all generalized multiresolution analyses Parseval frame wavelets all semi-orthogonal Parseval frame wavelets in . We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonical dual wavelet frame cannot be generated by the translations and dilations of a single function. Traits of tight wavelet frames are presented.

You might also be interested in these eBooks

Advances in Applied Materials and Electronics Engineering II

View Preview

Info:

Periodical:

Advanced Materials Research (Volume 684)

Pages:

663-666

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.684.663

Citation:

Cite this paper

Online since:

April 2013

Authors:

Jing Li Gao, Shi Hui Cheng

Keywords:

Banach Space, Canonical Frames, Dual Frame, Frame Operator, Multiresolution Analysis, Parseval Frame, Symmetric Tight Frames

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] Duffin R.J., and Schaeffer A.C., A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., Vol. 72, pp.341-366, (1952).

DOI: 10.1090/s0002-9947-1952-0047179-6

Google Scholar

[2] Daubechies I., Grossmann A., and Meyer Y., Painless nonorthogonal expansions, J. Math. Phys., Vol 27, No. 5, pp.1271-1283.

DOI: 10.1063/1.527388

Google Scholar

[3] Ron A., and Shen Z. W., Affine systems in (Ⅱ) Dual systems, Fourier Anal. Appl., Vol. 4, pp.617-637, (1997).

Google Scholar

[4] Chui C.K., etal., Nonstationary tight wavelet frames, I: Bounded intervals, Appl. Comput. Harmon. Anal., Vol. 17, pp.141-197, (2004).

DOI: 10.1016/j.acha.2004.02.004

Google Scholar

[5] Weber E., Orthogonal frames of translates,J. Appl. comput. Harmon. Anal., Vol. 17, pp.69-90, (2004).

Google Scholar

[6] Daubechies I., and B. Han. Pairs of dual wavelet frames from any two refinable functions, J. Constr. Appro., Vol. 20, pp.325-352, (2004).

DOI: 10.1007/s00365-004-0567-4

Google Scholar

[7] Chen Qingjiang, Liu Baocang, Cao Huaixin. Construction of a sort of multiple pseudoframes for subspaces with filter banks,. Chaos, Solitons & Fractals, 2009, 42(2): 801-808.

DOI: 10.1016/j.chaos.2009.02.019

Google Scholar

[8] Chen Qingjiang, Shi Zhi, Cao Huaixin. The characterization of a class of subspace pseudoframes with arbitrary real number translations,. Chaos, Solitons & Fractals, 2009, 42(5): 2696–2706.

DOI: 10.1016/j.chaos.2009.03.176

Google Scholar