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arXiv · 2111.13227

Spectral analysis and stabilization of the dissipative Schr\"{o}dinger operator on the tadpole graph

Kaïs Ammari·Rachid Assel
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Abstract

We consider the damped Schr\"odinger semigroup $e^{-it \frac{d^2}{dx^2}}$ on the tadpole graph ${\mathcal R}$. We first give a careful spectral analysis and an appropriate decomposition of the kernel of the resolvent. As a consequence and by showing that the generalized eigenfunctions form a Riesz basis of some subspace of $L^2({\mathcal R})$, we prove that the corresponding energy decay exponentially.

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Kaïs Ammari, Rachid Assel. 2021-11-25. Spectral analysis and stabilization of the dissipative Schr\"{o}dinger operator on the tadpole graph. https://arxiv.org/abs/2111.13227

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