A remark on the spectral synthesis property for hypersurfaces of $\textbf {R}^ n$
HTML articles powered by AMS MathViewer
- by Kang Hui Guo PDF
- Proc. Amer. Math. Soc. 121 (1994), 185-192 Request permission
Abstract:
Let M be an $(n - 1)$-dimensional manifold in ${R^n}$ with constant relative nullity. Using an estimate established in an earlier work of the author (Canad. Math. Bull. 36 (1993), 64-73), we present a greatly simplified proof of Müller’s result on the weak spectral synthesis property of M.References
- Yngve Domar, Sur la synthèse harmonique des courbes de $R^{2}$, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A875–A878 (French). MR 412738
- Yngve Domar, On the spectral synthesis problem for $(n-1)$-dimensional subsets of $\textbf {R}^{n},\,n\geq 2$, Ark. Mat. 9 (1971), 23–37. MR 324319, DOI 10.1007/BF02383635 —, On the spectral synthesis in ${R^n}, n \geq 2$, Lecture Notes in Math., vol. 779, Springer-Verlag, Berlin and New York, 1979, pp. 46-72.
- Yngve Domar, A $C^{\infty }$ curve of spectral non-synthesis, Mathematika 24 (1977), no. 2, 189–192. MR 473719, DOI 10.1112/S0025579300009098
- Kang Hui Guo, On the spectral synthesis property and its application to partial differential equations, Ark. Mat. 30 (1992), no. 1, 93–103. MR 1171097, DOI 10.1007/BF02384864
- Kang Hui Guo, On the $p$-thin problem for hypersurfaces of $\mathbf R^n$ with zero Gaussian curvature, Canad. Math. Bull. 36 (1993), no. 1, 64–73. MR 1205896, DOI 10.4153/CMB-1993-010-3
- Philip Hartman, On isometric immersions in Euclidean space of manifolds with non-negative sectional curvatures, Trans. Amer. Math. Soc. 115 (1965), 94–109. MR 202094, DOI 10.1090/S0002-9947-1965-0202094-9
- Bernard Marshall, The Fourier transforms of smooth measures on hypersurfaces of $\textbf {R}^{n+1}$, Canad. J. Math. 38 (1986), no. 2, 328–359. MR 833572, DOI 10.4153/CJM-1986-016-7
- Detlef Müller, On the spectral synthesis problem for hypersurfaces of $\textbf {R}^{N}$, J. Functional Analysis 47 (1982), no. 2, 247–280. MR 664338, DOI 10.1016/0022-1236(82)90107-0
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 185-192
- MSC: Primary 43A45; Secondary 46F99
- DOI: https://doi.org/10.1090/S0002-9939-1994-1185263-7
- MathSciNet review: 1185263