Spectral analysis and stabilization of the dissipative Schrödinger operator on the tadpole graph

2021/11/25 by Kaïs Ammari, Ammari, Kaïs, Rachid Assel +1 · 1 citation
Mathematics · #34B45 #34L25 #35B20 #35B40 #47A60 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2111.13227

openalex publication_date 2021/11/25 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We consider the damped Schrödinger semigroup e^{-it (d2)/(dx2)} 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 L²(\mathcal R), we prove that the corresponding energy decay exponentially.

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• Ground States of the Nonlinear Schrödinger Equation on the Tadpole Graph with a Repulsive Delta Vertex Condition

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