IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v42y2009i4p1959-1966.html
   My bibliography  Save this article

The characterization of vector-valued multivariate wavelet packets associated with a dilation matrix

Author

Listed:
  • Wang, Xiao-Feng
  • Gao, Hongwei
  • Jinshun, Feng

Abstract

In this work, we introduce the notion of vector-valued multiresolution analysis and vector-valued multivariate wavelet packets associated with an arbitrary integer-valued dilation matrix. A novel method for constructing higher-dimensional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas regarding the wavelet packets are provided. Orthogonality decomposition relation formulas of the space L2(Rs)r are obtained by constructing a series of subspaces of the vector-valued wavelet packets. Finally, several orthonormal wavelet packet bases of L2(Rs)r are constructed from these wavelet packets. Relation to some physical theories such as fractal theory and E-infinity theory is also discussed.

Suggested Citation

  • Wang, Xiao-Feng & Gao, Hongwei & Jinshun, Feng, 2009. "The characterization of vector-valued multivariate wavelet packets associated with a dilation matrix," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1959-1966.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:1959-1966
    DOI: 10.1016/j.chaos.2009.03.200
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077909004032
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2009.03.200?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Iovane, G., 2006. "Cantorian spacetime and Hilbert space: Part I—Foundations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 857-878.
    2. Le Moyne, L. & Freire, V. & Conde, D. Queiros, 2008. "Fractal dimension and scale entropy applications in a spray," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 696-704.
    3. Li, Yueling & Dai, Chaoshou, 2006. "A multifractal formalism in a probability space," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 57-73.
    4. El Naschie, M.S., 2006. "Hilbert space, the number of Higgs particles and the quantum two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 9-13.
    5. Chen, Qingjiang & Cheng, Zhengxing, 2007. "A study on compactly supported orthogonal vector-valued wavelets and wavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 1024-1034.
    6. El Naschie, M.S., 2005. "A guide to the mathematics of E-infinity Cantorian spacetime theory," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 955-964.
    7. Chen, Qingjiang & Shi, Zhi, 2008. "Biorthogonal multiple vector-valued multivariate wavelet packets associated with a dilation matrix," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 323-332.
    8. Iovane, Gerardo & Giordano, Paola, 2007. "Wavelets and multiresolution analysis: Nature of ε(∞) Cantorian space–time," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 896-910.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Qing-Jiang & Qu, Xiao-Gang, 2009. "Characteristics of a class of vector-valued non-separable higher-dimensional wavelet packet bases," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1676-1683.
    2. Chen, Qingjiang & Huo, Ailian, 2009. "The research of a class of biorthogonal compactly supported vector-valued wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 951-961.
    3. Iovane, Gerardo, 2009. "The set of prime numbers: Multiscale analysis and numeric accelerators," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1953-1965.
    4. Chen, Qingjiang & Shi, Zhi, 2008. "Construction and properties of orthogonal matrix-valued wavelets and wavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 75-86.
    5. Wu, Guochang & Cheng, Zhengxing & Li, Dengfeng & Zhang, Fangjuan, 2008. "Parseval frame wavelets associated with A-FMRA," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1233-1243.
    6. Iovane, Gerardo, 2008. "The set of prime numbers: Symmetries and supersymmetries of selection rules and asymptotic behaviours," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 950-961.
    7. Sun, Lei & Zhang, Xiaozhong, 2009. "A note on biorthogonality of the scaling functions with arbitrary matrix dilation factor," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 711-715.
    8. Li, Dengfeng & Wu, Guochang, 2009. "Construction of a class of Daubechies type wavelet bases," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 620-625.
    9. Yuan, De-you & Du, Shu-de & Cheng, Zheng-xing, 2009. "Design and properties of vector-valued wavelets associated with an orthogonal vector-valued scaling function," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1368-1376.
    10. Sun, Lei & Li, Gang, 2009. "Generalized orthogonal multiwavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2420-2424.
    11. Han, Jincang & Cheng, Zhengxing & Chen, Qingjiang, 2009. "A study of biorthogonal multiple vector-valued wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1574-1587.
    12. Iovane, Gerardo & Giordano, Paola, 2007. "Wavelets and multiresolution analysis: Nature of ε(∞) Cantorian space–time," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 896-910.
    13. Iovane, Gerardo, 2008. "The distribution of prime numbers: The solution comes from dynamical processes and genetic algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 23-42.
    14. Sun, Lei & Cheng, Zhengxing, 2007. "Construction of a class of compactly supported orthogonal vector-valued wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 253-261.
    15. Chen, Qingjiang & Shi, Zhi, 2008. "Biorthogonal multiple vector-valued multivariate wavelet packets associated with a dilation matrix," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 323-332.
    16. Chen, Qingjiang & Zhao, Yanhui & Gao, Hongwei, 2009. "Existence and characterization of orthogonal multiple vector-valued wavelets with three-scale," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2484-2493.
    17. Chen, Qingjiang & Cao, Huaixin & Shi, Zhi, 2009. "Construction and characterizations of orthogonal vector-valued multivariate wavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1835-1844.
    18. Wu, Guochang & Li, Zhiqiang & Cheng, Zhengxing, 2009. "Construction of wavelets with composite dilations," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2447-2456.
    19. Chen, Qingjiang & Cao, Huaixin & Shi, Zhi, 2009. "Construction and decomposition of biorthogonal vector-valued wavelets with compact support," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2765-2778.
    20. Iovane, G. & Chinnici, M. & Tortoriello, F.S., 2008. "Multifractals and El Naschie E-infinity Cantorian space–time," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 645-658.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:1959-1966. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.