Asymptotic behaviour of the spectrum of a waveguide with distant perturbations
نویسنده
چکیده
We consider the waveguide modelled by a n-dimensional infinite tube. The operator we study is the Dirichlet Laplacian perturbed by two distant perturbations. The perturbations are described by arbitrary abstract operators ”localized” in a certain sense, and the distance between their ”supports” tends to infinity. We study the asymptotic behaviour of the discrete spectrum of such system. The main results are a convergence theorem and the asymptotics expansions for the eigenvalues. The asymptotic behaviour of the associated eigenfunctions is described as well. We also provide some particular examples of the distant perturbations. The examples are the potential, second order differential operator, magnetic Schrödinger operator, curved and deformed waveguide, delta interaction, and integral operator.
منابع مشابه
Asymptotic behaviour of the spectrum of a waveguide with distant perturbation
We consider the waveguide modelled by n-dimensional tube in which Dirichlet Laplacian is considered perturbed by two distant perturbations. These perturbations are described by two arbitrary abstract operators which are ”localized” in some sense, and the distance between their ”supports” tends to infinity. We study the asymptotic behaviour of the discrete spectrum of such problem. The main resu...
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