scholarly journals Spectral analysis of the Schrödinger operator on binary tree-shaped networks and applications

2015 ◽  
Vol 259 (12) ◽  
pp. 6923-6959 ◽  
Author(s):  
Kaïs Ammari ◽  
Denis Mercier ◽  
Virginie Régnier
Keyword(s):  
Spectral Analysis ◽  
Schrödinger Operator ◽  
Binary Tree ◽  
Schrodinger Operator

A MOURRE ESTIMATE FOR A SCHRÖDINGER OPERATOR ON A BINARY TREE

2000 ◽  
Vol 12 (12) ◽  
pp. 1655-1667 ◽  
Author(s):  
C. ALLARD ◽  
R. FROESE
Keyword(s):  
Schrödinger Operator ◽  
Binary Tree ◽  
Invariant Subspaces ◽  
Schrodinger Operator ◽  
Conjugate Operator ◽  
Order Difference ◽  
First Order ◽  
Decay Condition ◽  
Mourre Estimate

Let G be a binary tree with vertices V and H be a Schrödinger operator acting on ℓ2 (V). A decomposition of the space ℓ2 (V) into invariant subspaces is exhibited yielding a conjugate operator A for use in the Mourre estimate. We show that for potentials q satisfying a first order difference decay condition, a Mourre estimate for H holds.

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