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Damping oscillatory integrals

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References

  1. Bruna, J., Nagel, A., Wainger, S.: Convex hypersurfaces and Fourier transforms. Ann. Math.127, 333–365 (1988)

    Google Scholar 

  2. Cowling, M., Disney, S.: On oscillatory integrals. In: Cowling, M., Meaney, C., Moran, W. (eds.) Miniconference on Harmonic Analysis (Canberra, 17–20 June 1987). (Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 15, pp. 45–54 Canberra: Centre for Mathematical Analysis 1987

    Google Scholar 

  3. Cowling, M., Mauceri, G.: Oscillatory integrals and Fourier transforms of surface carried measures. Trans. Am. Math. Soc.304, 53–68 (1987)

    Google Scholar 

  4. Herz, C.S.: Fourier transforms related to convex sets. Ann. Math.75, 81–92 (1962)

    Google Scholar 

  5. Hlawka, E.: Über Integrale auf konvexen Körper. I., Monatsh. Math.54, 1–36 (1950)

    Google Scholar 

  6. Hörmander, L.: The Analysis of Linear Partial Differential Operators, Volume I. Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  7. Jeanquartier, P.: Développement asymptotique de la distribution de Dirac. C.R. Acad. Sci. Paris271, 1159–1161 (1970)

    Google Scholar 

  8. John, F.: Extremum problems with inequalities as subsidiary conditions. In: Friedrichs, K. O., Neugebauer, O.E., Stoker, J.J. (eds.) Studies and Essays Presented to Richard Courant on his Sixtieth Birthday. January 8, 1948 (pp. 187–204) New York: Interscience 1948

    Google Scholar 

  9. Leichtweiß, K.: Über die affine Exzentrizität konvexer Körper. Arch. Math.10, 187–199 (1959)

    Google Scholar 

  10. Littman, W.: Fourier transforms of surface carried measures and differentiability of surface averages. Bull. Am. Math. Soc.69, 766–770 (1963)

    Google Scholar 

  11. Malgrange, B.: Intégrales asymptotiques et monodromies. Ann. Sci. Ec. Norm. Super.7, 405–430 (1974)

    Google Scholar 

  12. Randol, B.: On the asymptotic behaviour of the Fourier transform of the indicator function of a convex set. Trans. Am. Math. Soc.139, 279–285 (1969)

    Google Scholar 

  13. Sogge, C.D., Stein, E.M.: Averages of functions over hypersurfaces inR n Invent. Math.82, 543–556 (1985)

    Google Scholar 

  14. Stein, E.M.: Oscillatory integrals in Fourier analysis. In: Stein, E.M. (eds.) Beijing Lectures in Harmonic Analysis. (Ann. Math. Stud112, pp. 307–355) Princeton, N.J.: Princeton University 1986

    Google Scholar 

  15. Svensson, I.: Estimates for the Fourier transform of the characteristic function of a convex set. Ark. Mat.9, 11–22 (1971)

    Google Scholar 

  16. Varĉenko, A.N.: Newton polyhedra and estimation of oscillating integrals. Funct. Anal. Appl.10, 175–196 (1976)

    Google Scholar 

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Research supported by the Australian Research Council and the Italian Ministero della Pubblica Istruzione

Oblatum 13-IV-1989 & 5-VII-1989

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Cowling, M., Disney, S., Mauceri, G. et al. Damping oscillatory integrals. Invent Math 101, 237–260 (1990). https://doi.org/10.1007/BF01231503

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