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Continuous dependence of the transmission eigenvalues in one dimension

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  • The transmission eigenvalue problem on the interval $\left[ a,b\right] $ is considered. We show that the isolated transmission eigenvalues are continuous functions of the coefficients of the problem and that the transmission eigenfunctions can be normalized so that they depend continuously on all coefficients in the uniform norm. Throughout this work, our results are established without assumptions on the sign of the contrasts.
    Mathematics Subject Classification: Primary: 34B40, 34L25; Secondary: 78A25.

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