Skip to main content
SpringerLink
Log in

Analytic Representations of Tempered Distributions Using Wavelets

  • Chapter
Generalized Functions and Their Applications

  • 201 Accesses

Abstract

The properties of the analytic representations of distributions on the boundary of the unit disk are well understood. Trigonometric Fourier series constitute the principal tool used to construct and analyze them [5].

Research supported in part by NSF grant #DMS-901526

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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.

References

  1. H. Bremermann, “Distribution, Complex Variables, and Fourier Transforms,” Addison-Wesley, Reading, MA (1965).

    Google Scholar 

  2. I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 909–996 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  3. Y. Meyer, “Ondelettes et Opérateurs I,” Hermann, Paris (1990).

    MATH  Google Scholar 

  4. E. M. Stein and G. Weiss, “Fourier Analysis on Euclidean Spaces,” Princeton Univ. Press, Princeton, NJ (1971).

    MATH  Google Scholar 

  5. G. G. Walter, Local boundary behavior of harmonic functions, Ill. J. of Math. 16 491–501 (1980).

    Google Scholar 

  6. G. G. Walter, Hermite series as boundary values, Trans. AMS 218 155–171 (1976).

    Article  MATH  Google Scholar 

  7. G. G. Walter, Analytic representations with wavelet expansions, to appear in Journal of Complex Variables (1992).

    Google Scholar 

  8. G. G. Walter, Wavelets and generalized functions, in “Wavelets — A Tutorial in Theory and Applications” C. Chui, ed., Academic Press, New York (1992).

    Google Scholar 

  9. A. H. Zemanian, “Distribution theory and Transform Analysis,” Dover, New York (1965).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI, 53201, USA

    Gilbert G. Walter

Authors
  1. Gilbert G. Walter
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Banaras Hindu University, Varanasi, India

    R. S. Pathak

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Science+Business Media New York

About this chapter

Cite this chapter

Walter, G.G. (1993). Analytic Representations of Tempered Distributions Using Wavelets. In: Pathak, R.S. (eds) Generalized Functions and Their Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1591-7_27

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-1591-7_27

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-1593-1

  • Online ISBN: 978-1-4899-1591-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation