Resonances on regular tree graphs

27 Aug 2017  ·  Bourget Olivier, Sambou Diomba, Taarabt Amal ·

We investigate the distribution of the resonances near spectral thresholds of Laplace operators on regular tree graphs with $k$-fold branching, $k \geq 1$, perturbed by nonself-adjoint exponentially decaying potentials. We establish results on the absence of resonances which in particular involve absence of discrete spectrum near some sectors of the essential spectrum of the operators...

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Mathematical Physics Mathematical Physics Spectral Theory