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Christ, M..Restriction of the Fourier transform to submanifolds of low codimension, Ph.D. Thesis, University of Chicago, Illinois.
De Carli, L. and Iosevich, A. (1995). A restriction theorem for flat manifolds of codimension two,Illinois M.J. (to appear).
Greenleaf, A. (1982). Principal curvature and harmonic analysis,Indiana Math. J.,30, 519–537.
Gel'fand, I.M. and Shilov, G.E. (1964). Generalized Functions Vol., 1, Academic Press.
Hironaka, H. (1964). Resolution of singularities of an algebraic variety over a field of characteristic O,Annal. Math.,79, 109–203, 205–326.
Iosevich. A. (1994). Maximal operators associated to families of flat curves in the plane,Duke Math. J.,76.
Iosevich, A (1995). Maximal averages over homogeneous hypersurfaces in ℝ3,Forum Mathematicum (to appear).
Iosevich, A. and Sawyer, E. (1995). Oscillatory integrals and maximal averaging operators associated to homogeneous hypersurfaces,Duke Math. J. (to appear).
Littman, W. (1963). Fourier transforms of surface carried measures and differentiability of surface averages,Bull. Am. Math. Soc.,69, 766–770.
Rudin, W. (1973).Functional analysis, McGraw-Hill, New York.
Prestini, E. (1979). Restriction theorems for the Fourier transform to some manifolds in ℝn,Proc. Symp. Pure Math., XXXV Part 1.
Shintani, T. (1975). On zeta function associated with the vector space of quadratic forms,J. F. Sc. U. Tokyo, 25–65.
Sogge, C.D. (1991).Fourier Integrals in Classical Analysis, Oxford University Press.
Stein, E.M. (1993).Harmonic Analysis, Princeton University Press,43, Princeton, NJ.
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Communicated by John J. Benedetto
Acknowledgements and Notes. This work was supported in part by NSF Grant DMS97 0682S.
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De Carli, L., Iosevich, A. Some sharp restriction theorems for homogeneous manifolds. The Journal of Fourier Analysis and Applications 4, 105–128 (1998). https://doi.org/10.1007/BF02475930
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DOI: https://doi.org/10.1007/BF02475930