Skip to main content
SpringerLink
Log in

What Is It Possible to Say About an Asymptotic of the Fourier Transform of the Characteristic Function of a Two-dimensional Convex Body with Nonsmooth Boundary?

  • Chapter
  • First Online:
Fourier Analysis and Convexity

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

There are two problems about the behavior of integrals

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
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. Brandolini, L., Colzani, L., Iosevich, A., Podkorytov, A., and Travaglini, G., Geometry of the Gauss map and lattice points in convex domains, Mathematika, 48 (2001), 107–117.

    Article  MathSciNet  Google Scholar 

  2. Gutierrez Gonzales E.G., A lower bound for two-dimensional Lebesgue constants, Vestnik St. Peterburg Univ. Math., 26 (1993), 69–71.

    MathSciNet  MATH  Google Scholar 

  3. Herz, C.S., Fourier transforms related to convex sets, Ann. of Math., 75, no. 1 (1962), 81–92.

    Article  MathSciNet  Google Scholar 

  4. Kendall, D.G., On the number of lattice points inside a random oval, Quart. J., 19 (1948), 1–26.

    MathSciNet  MATH  Google Scholar 

  5. Podkorytov, A.N., The asymptotics of a Fourier transform on a convex curve, Vestnik Leningrad Univ. Math., 24 (1991), 57–65.

    MathSciNet  MATH  Google Scholar 

  6. Randol, B., On the Fourier transform of the indicator function of a planar set, Trans. Amer. Math. Soc.,139 (1969), 271–278.

    MathSciNet  MATH  Google Scholar 

  7. Randol, B., On the asymptotic behavior of the Fourier transform of the indicator func-tion of a convex set, Trans. Amer. Math. Soc., 139 (1969), 279–285.

    Article  MathSciNet  Google Scholar 

  8. Svensson, I., Estimates for the Fourier transform of the characteristic function of a convex set, Arkiv för Matematik,9, no. 1 (1971), 11–22.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, St.Petersburg State University, Bibliotecnaya pl. 2, Peterhof, St. Petersburg, 198904, Russia

    A. N. Podkorytov

Authors
  1. A. N. Podkorytov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Ingegneria Gestionale e dell’ Informazione, Università di Bergamo, Dalmine, 24044, Italy

    Luca Brandolini

  2. Dipartimento di Matematica e Applicazioni, UniversitĂ  di Milano-Bicocca, Milano, 20126, Italy

    Leonardo Colzani  & Giancarlo Travaglini  & 

  3. Department of Mathematics, University of Missouri-Columbia, Columbia, MO, 65211, USA

    Alex Iosevich

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Science+Business Media New York

About this chapter

Cite this chapter

Podkorytov, A.N. (2004). What Is It Possible to Say About an Asymptotic of the Fourier Transform of the Characteristic Function of a Two-dimensional Convex Body with Nonsmooth Boundary?. In: Brandolini, L., Colzani, L., Travaglini, G., Iosevich, A. (eds) Fourier Analysis and Convexity. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8172-2_9

Download citation

  • DOI: https://doi.org/10.1007/978-0-8176-8172-2_9

  • Published:

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6474-3

  • Online ISBN: 978-0-8176-8172-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation