ArticleOriginal scientific text
Title
Fourier transform of characteristic functions and Lebesgue constants for multiple Fourier series
Authors 1
Affiliations
- Dipartimento di Matematica dell'Università, via C. Saldini, 50, 20133 Milano, Italy
Bibliography
- L. Brandolini, Estimates for Lebesgue constants in dimension two, Ann. Mat. Pura Appl. (4) 156 (1990), 231-242.
- M. Carenini and P. M. Soardi, Sharp estimates for Lebesgue constants, Proc. Amer. Math. Soc. 89 (1983), 449-452.
- D. I. Cartwright and P. M. Soardi, Best conditions for the norm convergence of Fourier series, J. Approx. Theory 38 (1983), 344-353.
- E. T. Copson, Asymptotic Expansions, The University Press, Cambridge 1965.
- S. Giulini and G. Travaglini, Sharp estimates for Lebesgue constants on compact Lie groups, J. Funct. Anal. 68 (1986), 106-110.
- C. S. Herz, Fourier transforms related to convex sets, Ann. of Math. (2) 75 (1962), 81-92.
- W. Littman, Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. Amer. Math. Soc. 69 (1963), 766-770.
- J. Milnor, Morse Theory, Princeton University Press, 1963.
- F. W. J. Olver, Introduction to Asymptotics and Special Functions, Academic Press, New York 1974.
- B. Randol, On the Fourier transform of the indicator function of a planar set, Trans. Amer. Math. Soc. 139 (1969), 271-278.
- B. Randol, On the asymptotic behavior of the Fourier transform of the indicator function of a convex set, ibid., 279-285.
- 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.
- E. M. Stein, Problems in harmonic analysis related to curvature and oscillatory integrals, in: Proc. Internat. Congress Math. 1986, Vol. I, 196-221.
- A. A. Yudin and V. A. Yudin, Discrete imbedding theorems and Lebesgue constants, Math. Notes 22 (1977), 702-711.
- V. A. Yudin, Behavior of Lebesgue constants, ibid. 17 (1975), 233-235.