ArticleOriginal scientific text

Title

Fourier transform of characteristic functions and Lebesgue constants for multiple Fourier series

Authors 1

Affiliations

  1. Dipartimento di Matematica dell'Università, via C. Saldini, 50, 20133 Milano, Italy

Bibliography

  1. L. Brandolini, Estimates for Lebesgue constants in dimension two, Ann. Mat. Pura Appl. (4) 156 (1990), 231-242.
  2. M. Carenini and P. M. Soardi, Sharp estimates for Lebesgue constants, Proc. Amer. Math. Soc. 89 (1983), 449-452.
  3. D. I. Cartwright and P. M. Soardi, Best conditions for the norm convergence of Fourier series, J. Approx. Theory 38 (1983), 344-353.
  4. E. T. Copson, Asymptotic Expansions, The University Press, Cambridge 1965.
  5. S. Giulini and G. Travaglini, Sharp estimates for Lebesgue constants on compact Lie groups, J. Funct. Anal. 68 (1986), 106-110.
  6. C. S. Herz, Fourier transforms related to convex sets, Ann. of Math. (2) 75 (1962), 81-92.
  7. W. Littman, Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. Amer. Math. Soc. 69 (1963), 766-770.
  8. J. Milnor, Morse Theory, Princeton University Press, 1963.
  9. F. W. J. Olver, Introduction to Asymptotics and Special Functions, Academic Press, New York 1974.
  10. B. Randol, On the Fourier transform of the indicator function of a planar set, Trans. Amer. Math. Soc. 139 (1969), 271-278.
  11. B. Randol, On the asymptotic behavior of the Fourier transform of the indicator function of a convex set, ibid., 279-285.
  12. E. M. Stein, Oscillatory integrals in Fourier analysis, in: Beijing Lectures in Harmonic Analysis, Ann. of Math. Stud. 112, Princeton University Press, 1986, 307-355.
  13. E. M. Stein, Problems in harmonic analysis related to curvature and oscillatory integrals, in: Proc. Internat. Congress Math. 1986, Vol. I, 196-221.
  14. A. A. Yudin and V. A. Yudin, Discrete imbedding theorems and Lebesgue constants, Math. Notes 22 (1977), 702-711.
  15. V. A. Yudin, Behavior of Lebesgue constants, ibid. 17 (1975), 233-235.
Pages:
51-59
Main language of publication
English
Received
1992-09-23
Published
1993
Exact and natural sciences