Spectral and Dynamical Analysis of Fractional Discrete Laplacians on the Half-Lattice
We investigate discrete fractional Laplacians defined on the half-lattice in several dimensions, allowing possibly different fractional orders along each coordinate direction. By expressing the half-lattice operator as a boundary restriction of the full-lattice one plus a bounded correction that is relatively compact with respect to it, we show that both operators share the same essential spectrum and the same interior threshold structure. For perturbations by a decaying potential, the conjugat…
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