Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-24T00:56:56.224Z Has data issue: false hasContentIssue false
  • English
  • Français

A Uniform L∞ Estimate of the Smoothing Operators Related to Plane Curves

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., e-mail: kag026f@cnas.smsu.edutelephone: 417-836-6712
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In dealing with the spectral synthesis property for a plane curve with nonzero curvature, a key step is to have a uniform L∞ estimate for some smoothing operators related to the curve. In this paper, we will show that the same L∞ estimate holds true for a plane curve that may have zero curvature.

Keywords

Primary: 42B20secondary: 42B15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 4 , 01 December 1997 , pp. 433 - 442
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Domar, Y., Sur la synthese harmonique des courbes de R2. C. R. Acad. Sci. Paris Sér. I Math. 270 (1970), 875–878.Google Scholar
2. Domar, Y., On the spectral synthesis problem for (n − 1)-dimensional subsets of Rn, n ½ 2. Ark. Mat. 9 (1971), 23–37.Google Scholar
3. Domar, Y., On the spectral synthesis for curves in R3. Math. Scand. 39 (1976), 282–294.Google Scholar
4. Domar, Y., A C1 curve of spectral non-synthesis. Mathematika 24 (1977), 189–192.Google Scholar
5. Domar, Y., On the spectral synthesis in Rn, n ½ 2. Lecture Notes inMath. 779, Springer-Verlag, Berlin and New York, 1979, 46–72.Google Scholar
6. Guo, K., On the p-approximate property for hypersurfaces of Rn. Math. Proc. Cambridge Philos. Soc. 105 (1989), 503–511.Google Scholar
7. Guo, K., A remark on the spectral synthesis property for hypersurfaces of Rn. Proc. Amer. Math. Soc. 121 (1994), 185–192.Google Scholar
8. Gustavsson, R., On the spectral synthesis problem for curves in R3. Dept. of Math., Univ. of Uppsala, Research Report No. 6, 1974.Google Scholar
9. Herz, C. S., Spectral synthesis for the circle. Ann. Math. 68 (1958), 709–712.Google Scholar
10. Müller, D., On the spectral synthesis problem for hypersurfaces of RN. J. Funct. Anal. 47 (1982), 247–280.Google Scholar
11. Schwartz, L., Theorie des distributions. Tome 1, Paris, 1951.Google Scholar
12. Varopoulos, N .Th., Spectral synthesis on spheres. Proc. Cambridge Philos. Soc. 62 (1966), 379–387.Google Scholar