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arXiv · 2410.11729

Airy and Schr\"odinger-type equations on looping-edge graphs and applications

Jaime Angulo Pava·Alexander Muñoz
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Abstract

The aim of this work is to study the Airy and Schr\"odinger operators on looping-edge graphs, a class of metric graphs consisting of a circle and a finite number $N$ of infinite half-lines attached to a common vertex. For the Airy operator, we characterize all extensions generating unitary and contractive dynamics in terms of self-orthogonal subspaces and linear operators acting on indefinite inner product spaces (Krein spaces) associated to the boundary values at the vertex. Employing similar abstract techniques, we then describe a systematic way to produce self-adjoint extensions of the Schr\"odinger operator that are compatible with prescribed boundary relations on looping-edge and $\mathcal{T}$-shaped graphs.

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Jaime Angulo Pava, Alexander Muñoz. 2024-10-15. Airy and Schr\"odinger-type equations on looping-edge graphs and applications. https://arxiv.org/abs/2410.11729

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