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The asymptotic behavior of a Fourier transform and the localization property for eigenfunction expansions for some partial differential operators


Author: Burton Randol
Journal: Trans. Amer. Math. Soc. 168 (1972), 265-271
MSC: Primary 42A68; Secondary 35P10, 42A62, 47F05
DOI: https://doi.org/10.1090/S0002-9947-1972-0296600-X
MathSciNet review: 0296600
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Abstract: The asymptotic behavior of a certain Fourier transform is investigated, and the result is applied to obtain a localization theorem for elliptic operators on the torus.


References [Enhancements On Off] (What's this?)

  • [1] S. Bochner, Summation of multiple Fourier series by spherical means, Trans. Amer. Math Soc. 40 (1936), 175-207. MR 1501870
  • [2] A. Erdélyi, Asymptotic expansions, Dover, New York, 1956. MR 17, 1202. MR 0078494 (17:1202c)
  • [3] G. H. Hardy and Marcel Riesz, The general theory of Dirichlet's series, Cambridge Univ. Press, Cambridge, 1952.
  • [4] C. S. Herz, Fourier transforms related to convex sets, Ann. of Math. (2) 75 (1962), 81-92. MR 26 #545. MR 0142978 (26:545)
  • [5] E. Hlawka, Über Integrale auf konvexen Körpern. I, Monatsh. Math. 54 (1950), 1-36. MR 12, 197. MR 0037003 (12:197e)
  • [6] Walter Littman, Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. Amer. Math. Soc. 69 (1963), 766-770. MR 27 #5086. MR 0155146 (27:5086)
  • [7] E. M. Stein, Localization and summability of multiple Fourier series, Acta Math. 100 (1958), 93-147. MR 21 #4331. MR 0105592 (21:4331)
  • [8] Burton Randol, On the Fourier transform of the indicator function of a planar set, Trans. Amer. Math. Soc. 139 (1969), 271-278. MR 40 #4678a. MR 0251449 (40:4678a)
  • [9] -, On the asymptotic behavior of the Fourier transform of the indicator function of a convex set, Trans. Amer. Math. Soc. 139 (1969), 279-285. MR 40 #4678b. MR 0251450 (40:4678b)
  • [10] Ingvar Svensson, Estimates for the Fourier transform of the characteristic function of a convex set, Ark. Mat. 9 (1971), 11-22. MR 0328471 (48:6813)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0296600-X
Keywords: Asymptotic behavior of a Fourier transform, localization property for eigenfunction expansions
Article copyright: © Copyright 1972 American Mathematical Society

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