Skip to main content
SpringerLink
Log in

Estimates for the Fourier transform of the indicator function for nonconvex domains

  • Published:
Functional Analysis and Its Applications Aims and scope

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. C. S. Herz, “Fourier transforms related to convex set,” Ann. Math.,75, No. 2, 215–254 (1962).

    Google Scholar 

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

    Google Scholar 

  3. B. Randol, “On the asymptotic behavior of the Fourier transform of the indicator function of a convex set,” Trans. Am. Math. Soc.,139, 278–285 (1969).

    Google Scholar 

  4. I. Svensson, “Estimates for the Fourier transform of the characteristic function of a convex set,” Ark. Mat.,9, No. 1, 11–22 (1970).

    Google Scholar 

  5. Y. Colin de Verdière, “Nombre de points entiers dans une famille homothétique de domains de ℝn,” Ann. Sci. École Norm. Sup. (4),10, No. 4, 559–575 (1977).

    Google Scholar 

  6. A. N. Varchenko, “The number of lattice points in families of homothetic domains in ℝn,” Funkts. Anal. Prilozhen.,17, No. 2, 1–6 (1983).

    Google Scholar 

  7. V. I. Arnold, S. M. Gusein-Zade, and A. N. Varchenko, Singularities of Differentiable Maps. Vol. I. The Classification of Critical Points, Caustics, and Wave Fronts [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  8. B. Malgrange, Ideals of Differentiable Functions, Oxford Univ. Press (1966).

  9. J. Duistermaat, “Oscillatory integrals, Lagrange immersions and unifoldings of singularities,” Comm. Pure Appl. Math.,27, No. 2, 207–281 (1974).

    Google Scholar 

  10. J. N. Mather, “Stability ofC ∞ mappings. II: Infinitesimal stability implies stability,” Ann. Math.,89, No. 2, 254–291 (1969).

    Google Scholar 

  11. V. N. Karpushkin, “Uniform estimates of oscillating integrals with a parabolic or a hyperbolic phase,” Trudy Sem. Petrovsk.,9, 3–39 (1983).

    Google Scholar 

  12. V. I. Arnold, Singularities of smooth mappings, Usp. Mat. Nauk,23, No. 1, 3–44 (1968).

    Google Scholar 

  13. V. I. Arnold, “Normal forms of functions near degenerate critical points, Weyl groups ofA k ,D k , andE k , and Lagrange singularities,” Funkts. Anal. Prilozhen.,6, No. 4, 3–25 (1972).

    Google Scholar 

  14. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  15. I. A. Ikromov, “Invariant estimates for two-dimensional trigonometric integrals,” Mat. Sb.,180, No. 8, 1017–1032 (1989).

    Google Scholar 

Download references

Authors
  1. I. A. Ikromov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Tashkent State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 29, No. 3, pp. 16–24, July–September, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ikromov, I.A. Estimates for the Fourier transform of the indicator function for nonconvex domains. Funct Anal Its Appl 29, 161–167 (1995). https://doi.org/10.1007/BF01077049

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01077049

Keywords

Search

Navigation