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

  • N.K. Chakravarty (a1) and Sudip Kumar Acharyya (a1)

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.

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References

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1Ambarzumyan, V. A.. Uber eine Frage der Eigenvert theoric. Z. Phys. 53 (1929), 690695.
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), 1942.
3Chakravarty, N. K.. Some problems in eigenfunction expansions (I). Quart. J. Math. Oxford 16 (1965), 135150.
4Chakravarty, N. K.. Some problems in eigenfunction expansions II. Quart. J. Math. Oxford 19 (1968), 213224.
5Titchmarsh, E. C.. Eigenfunction expansions associated with second order differential equations Part I, 2nd edition (Oxford: Oxford University Press, 1962).
6Levitan, B. M. and Gasymov, M. G.. Determination of a differential equation by two of its spectra. Uspekhi Mat. Nauk 19 (1964), 363.
7Paladhi, Basudeb Ray. The inverse problem associated with a pair of second order differential equations. Proc. London Math. Soc. (3) 43 (1981), 169192.

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