Abstract
We study the eigenvalues of two restrictions ofB∂ x +P whereB is the two-by-two matrix that is zero on the diagonal and one off the diagonal andP is a two-by-two matrix of Lipschitz functions on the unit interval. We establish asymptotic forms for their eigenvalues and associated root vectors and demonstrate that these root vectors constitute a Riesz basis inL 2(0, 1)2. We show that our forward analysis makes rigorous the attack on the associated inverse problem by M. Yamamoto,Inverse spectral problem for systems of ordinary differential equations of first order, I, J. Fac. Sci. Univ. Tokyo, Sect. 1A, Math. 35, 1988, pp. 519–546. We apply these results to the recovery of the line resistance and leakage conductance of a nonuniform transmission line.
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Supported by NSF grant DMS-9258312.