## A remark on the spectral synthesis property for hypersurfaces of $\textbf {R}^ n$

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- 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
—, - 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

*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.

## 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