Inverse spectral problems for non-selfadjoint second-order differential operators with Dirichlet boundary conditions

[[abstract]]We study the inverse problem for non-selfadjoint Sturm-Liouville operators on a finite interval with possibly multiple spectra. We prove the uniqueness theorem and obtain constructive procedures for solving the inverse problem along with the necessary and sufficient conditions of its solvability and also prove the stability of the solution.[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]電子版[[countrycodes]]DE

Estimates of complex eigenvalues and an inverse spectral problem for the transmission eigenvalue problem

This work deals with the interior transmission eigenvalue problem: y 00 + k 2η (r) y = 0 with boundary conditions y (0) = 0 = y 0 (1) sin k k − y (1) cos k, where the function η(r) is positive. We obtain the asymptotic distribution of non-real transmission eigenvalues under the suitable assumption on the square of the index of refraction η(r). Moreover, we provide a uniqueness theorem for the case R 1 0 p η(r)dr > 1, by using all transmission eigenvalues (including their multiplicities) along with a partial information of η(r) on the subinterval. The relationship between the proportion of the needed transmission eigenvalues and the length of the subinterval on the given η(r) is also obtained