Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T01:58:22.308Z Has data issue: false hasContentIssue false
  • English
  • Français

On an extension of the theorem of V. A. Ambarzumyan

Published online by Cambridge University Press:  14 November 2011

N.K. Chakravarty  and
Sudip Kumar Acharyya
N.K. Chakravarty
Affiliation:
Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Calcutta-700 019, India
Sudip Kumar Acharyya
Affiliation:
Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Calcutta-700 019, India
Get access Rights & Permissions [Opens in a new window]

Synopsis

The Ambarzumyan theorem connecting the Sturm–Liouville problem and the corresponding problem associated with the Fourier differential equation is extended to a class of second order matrix differential systems.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 1-2 , 1988 , pp. 79 - 84
Copyright
Copyright © Royal Society of Edinburgh 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Ambarzumyan, V. A.. Uber eine Frage der Eigenvert theoric. Z. Phys. 53 (1929), 690–695.CrossRefGoogle Scholar
2Chakravarty, N. K. and Sengupta, P. K.. On the distribution of the eigenvalues of a matrix differential operator. J. Indian Inst. Sci. (B) 61 (1979), 19–42.Google Scholar
3Chakravarty, N. K.. Some problems in eigenfunction expansions (I). Quart. J. Math. Oxford 16 (1965), 135–150.Google Scholar
4Chakravarty, N. K.. Some problems in eigenfunction expansions II. Quart. J. Math. Oxford 19 (1968), 213–224.CrossRefGoogle Scholar
5Titchmarsh, E. C.. Eigenfunction expansions associated with second order differential equations Part I, 2nd edition (Oxford: Oxford University Press, 1962).Google Scholar
6Levitan, B. M. and Gasymov, M. G.. Determination of a differential equation by two of its spectra. Uspekhi Mat. Nauk 19 (1964), 3–63.Google Scholar
7Paladhi, Basudeb Ray. The inverse problem associated with a pair of second order differential equations. Proc. London Math. Soc. (3) 43 (1981), 169–192.Google Scholar