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

Luca Brandolini

Colloquium Mathematicae (1993)

  • Volume: 65, Issue: 1, page 51-59
  • ISSN: 0010-1354

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Brandolini, Luca. "Fourier transform of characteristic functions and Lebesgue constants for multiple Fourier series." Colloquium Mathematicae 65.1 (1993): 51-59. <http://eudml.org/doc/210204>.

@article{Brandolini1993,
author = {Brandolini, Luca},
journal = {Colloquium Mathematicae},
keywords = {characteristic function; Fourier transform; multiple Fourier series; Lebesgue constants; oscillatory integrals},
language = {eng},
number = {1},
pages = {51-59},
title = {Fourier transform of characteristic functions and Lebesgue constants for multiple Fourier series},
url = {http://eudml.org/doc/210204},
volume = {65},
year = {1993},
}

TY - JOUR
AU - Brandolini, Luca
TI - Fourier transform of characteristic functions and Lebesgue constants for multiple Fourier series
JO - Colloquium Mathematicae
PY - 1993
VL - 65
IS - 1
SP - 51
EP - 59
LA - eng
KW - characteristic function; Fourier transform; multiple Fourier series; Lebesgue constants; oscillatory integrals
UR - http://eudml.org/doc/210204
ER -

References

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  1. [1] L. Brandolini, Estimates for Lebesgue constants in dimension two, Ann. Mat. Pura Appl. (4) 156 (1990), 231-242. Zbl0778.42008
  2. [2] M. Carenini and P. M. Soardi, Sharp estimates for Lebesgue constants, Proc. Amer. Math. Soc. 89 (1983), 449-452. Zbl0523.42009
  3. [3] D. I. Cartwright and P. M. Soardi, Best conditions for the norm convergence of Fourier series, J. Approx. Theory 38 (1983), 344-353. Zbl0516.42020
  4. [4] E. T. Copson, Asymptotic Expansions, The University Press, Cambridge 1965. 
  5. [5] S. Giulini and G. Travaglini, Sharp estimates for Lebesgue constants on compact Lie groups, J. Funct. Anal. 68 (1986), 106-110. Zbl0664.22008
  6. [6] C. S. Herz, Fourier transforms related to convex sets, Ann. of Math. (2) 75 (1962), 81-92. Zbl0111.34803
  7. [7] W. Littman, Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. Amer. Math. Soc. 69 (1963), 766-770. Zbl0143.34701
  8. [8] J. Milnor, Morse Theory, Princeton University Press, 1963. 
  9. [9] F. W. J. Olver, Introduction to Asymptotics and Special Functions, Academic Press, New York 1974. Zbl0308.41023
  10. [10] B. Randol, On the Fourier transform of the indicator function of a planar set, Trans. Amer. Math. Soc. 139 (1969), 271-278. Zbl0183.26904
  11. [11] B. Randol, On the asymptotic behavior of the Fourier transform of the indicator function of a convex set, ibid., 279-285. 
  12. [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. [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. [14] A. A. Yudin and V. A. Yudin, Discrete imbedding theorems and Lebesgue constants, Math. Notes 22 (1977), 702-711. Zbl0418.42005
  15. [15] V. A. Yudin, Behavior of Lebesgue constants, ibid. 17 (1975), 233-235. Zbl0321.42016

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