Perturbations of embedded eigenvalues for self-adjoint ODE systems

2021/06/07 by Sasane, Sara Maad, Papalazarou, Alexia
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2106.03574

Abstract

We consider a perturbation problem for embedded eigenvalues of a self-adjoint differential operator in L²(\mathbb R;\mathbb Rⁿ). In particular, we study the set of all small perturbations in an appropriate Banach space for which the embedded eigenvalue remains embedded in the continuous spectrum. We show that this set of small perturbations forms a smooth manifold and we specify its co-dimension. Our methods involve the use of exponential dichotomies, their roughness property and Lyapunov-Schmidt reduction.

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