Skip to main content

The Continuous Wavelet Transform in Clifford Analysis

  • Chapter
Clifford Analysis and Its Applications

Part of the book series: NATO Science Series ((NAII,volume 25))

Abstract

A theory of higher dimensional continuous wavelet transforms in Clifford analysis is presented. The construction of Clifford-Hermite wavelets generates new generalized Hermite polynomials.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Refbrences

  1. L. Andersson, B. Jawerth and M. Mitrea: The Cauchy singular integral operator and Clifford wavelets, in: J. J. Benedetto and M. W. Frazier (eds.): Wavelets: mathematics and applications, CRC Press, 1994, 525–546

    Google Scholar 

  2. J.-P. Antoine, R. Murenzi and P. Vandergheynst: Two-dimensional directional wavelets in image processing, Int. J. of Imaging Systems and Technology, 7, 152–165

    Google Scholar 

  3. F. Brackx, R. Delanghe and F. Sommen: Clifford analysis, Pitman Publ., 1982

    Google Scholar 

  4. F. Brackx and F. Sommen: Clifford-Hermite Wavelets in Euclidean Space, Journal of Fourier Analysis and Applications, volume 6, no 3, 2000, 299–310

    Article  MathSciNet  MATH  Google Scholar 

  5. F. Brackx and F. Sommen: Clifford-Hermite Wavelets in Euclidean Space, to appear in the Proceedings of the Conference on Dirac Operators and Applications, Cetraro (Italy), October 4-10, 1998

    Google Scholar 

  6. L. Cohen: General phase-space distribution functions, J. Math. Phys., 7, 781–786, 1966

    Article  Google Scholar 

  7. I. Daubechies: Ten Lectures on Wavelets, SIAM, Philadelphia, 1992

    Book  MATH  Google Scholar 

  8. D. Marr: Vision, Freeman, San Francisco, 1982

    Google Scholar 

  9. O. Rioul and M. Vetterli: Wavelets and signal processing, IEEE SP Magazine, October 1991, 14–38

    Google Scholar 

  10. F. Sommen: Special Functions in Clifford analysis and Axial Symmetry, Journal of Math. Analysis and Applications, 130, no 1, 1988, 110–133

    Article  MathSciNet  MATH  Google Scholar 

  11. D. Walnut: Application of Gabor and wavelet expansions to the Radon transform, Probabilistic and Stochastic Methods in Analysis, with Applications, NATO ASI Series, J. Byrnes et al., eds., Kluwer Academic Publishers, The Netherlands, 1992, 187–205

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Brackx, F., Sommen, F. (2001). The Continuous Wavelet Transform in Clifford Analysis. In: Brackx, F., Chisholm, J.S.R., Souček, V. (eds) Clifford Analysis and Its Applications. NATO Science Series, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0862-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0862-4_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-7045-1

  • Online ISBN: 978-94-010-0862-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics