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

• Autorzy: Luca Brandolini
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 65
• Numer: 1
• Strony: 51-59

Daty

wydano

1993

otrzymano

1992-09-23

Twórcy

autor

Luca Brandolini

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

Bibliografia

• [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.