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On the p-Thin Problem for Hypersurfaces of Rn With Zero Gaussian Curvature

Published online by Cambridge University Press:  20 November 2018

Kanghui Guo
Kanghui Guo*
Affiliation:
Department of Mathematics Southwest Missouri State University Springfield, Missouri 65804 U.S.A.
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Abstract

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A subset M of Rn is said to be p-thin if T ∊ FLP(Rn) and supp(T) ⊂ M imply T = 0. For a class of smooth (n — 1 )-dimensional submanifolds of Rn, we obtain the optimal result for the p-thin problem, which is applied to give the complete solution to a uniqueness problem of wave equations.

Keywords

43A45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 1 , 01 March 1993 , pp. 64 - 73
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Domar, Y., On the spectral synthesis problem for (n— \)-dimensional subsets of Rn, n ≥ 2, Arkiv fur matematik 9(1971), 23–37.Google Scholar
2. Domar, Y., On the spectral synthesis in Rn, n ≥ 2, Lecture Notes in Mathematics, 779, Springer-Verlag, 46–72.Google Scholar
3. Guo, K., A note on the spectral synthesis property and its application to partial differential equations, Arkiv fur matematik 30(1992), 93–103.Google Scholar
4. Hartman, R, On the isometric immersions in Euclidian space of manifolds with non-negative sectional curvatures,Trzns. Amer. Math. Soc. 115(1965),94–109.Google Scholar
5. Hormander, L., Lower bounds at infinity for solutions of differential equations with constant coefficients, Israel J. Math. 16(1973), 103–116.Google Scholar
6. Hormander, L., The analysis of linear partial differential operators I, Springer-Verlag, 1983.Google Scholar
7. Kenig, C. E., Ruiz, A. and Sogge, C. D., Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators, Duke Math. J. 55(1987), 329–347.Google Scholar
8. Littman, W., Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. Amer. Math. Soc. 69(1963), 766–770.Google Scholar
9. Lust, F., Le Problème de la synthèse et de la p-finesse pour certain orbites des groupes lineares dans Ap(Rn), Studia Math. 39(1971), 17–28.Google Scholar
10. Marshall, B., The Fourier transform of smooth measures on hypersurfaces of Rn+1 , Can. J. Math. 38(1986), 328–359.Google Scholar
11. Miiller, D., On the spectral synthesis problem for hypersurfaces of RN , Journal of Functional Analysis 47(1982), 247–280.Google Scholar
12. Stein, E. M., Oscillatory integrals in Fourier Analysis, Beijing Lectures in Harmonic Analysis, 1986,307- 355.Google Scholar