SPECTRAL ANALYSIS OF THE SCHRÖDINGER OPERATOR ON BINARY TREE-SHAPED NETWORKS AND APPLICATIONS

Kaïs Ammari (1) , Denis Mercier (2) , Virginie Régnier (2)

1 Département de Mathématiques [Monastir]
2 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

In this paper we analyse the spectrum of the dissipative Schrödinger operator on binary tree-shaped net-works. As applications, we study the stability of the Schrödinger system using a Riesz basis as well as the transfer function associated to the system.

Mots clés: tree; transfer function; dissipative Schr\"odinger operator; Riesz basis; boundary feedback stabilization

Domaines: Equations aux dérivées partielles [math.AP]

Kaïs Ammari, Denis Mercier, Virginie Régnier. SPECTRAL ANALYSIS OF THE SCHRÖDINGER OPERATOR ON BINARY TREE-SHAPED NETWORKS AND APPLICATIONS. 2015. ⟨hal-01109134⟩