Hostname: page-component-7479d7b7d-fwgfc Total loading time: 0 Render date: 2024-07-11T02:02:59.933Z Has data issue: false hasContentIssue false
  • English
  • Français

Eigenvalues of smooth positive definite kernels

Published online by Cambridge University Press:  20 January 2009

J. B. Reade
J. B. Reade
Affiliation:
Mathematics DepartmentManchester UniversityManchesterM13 9PL, England
Rights & Permissions [Opens in a new window]

Extract

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.

For positive definite C1 kernels on a finite real interval the eigenvalues λn are known to be o(1/n2). In this paper this result is shown to be best possible in the best possible sense, namely that, given any decreasing sequence λn, which is o(1/n2), there exist positive definite C1 kernels whose eigenvalues are λn.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 1 , February 1992 , pp. 41 - 45
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

1.Chaundy, T. W. and Jolliffe, A. E., The uniform convergence of a certain class of trigonometrical series, Proc. London Math. Soc. (2), 15 (1916), 214–216.Google Scholar
2.Reade, J. B., Eigenvalues of smooth kernels, Math. Proc. Cambridge Philos. Soc. 95 (1984), 135–140.CrossRefGoogle Scholar
3.Reade, J. B., On the sharpness of Weyl's estimate for the eigenvalues of smooth kernels, SIAM J. Math. Anal. 16 (1985), 548–550.CrossRefGoogle Scholar
4.Reade, J. B., Positive definite Cp kernels, SIAM J. Math. Anal. 17 (1986), 420–421.CrossRefGoogle Scholar
5.Titchmarsh, E. C., Theory of Functions (Oxford University Press, 1932).Google Scholar