Laplace and Schrödinger operators on regular metric trees: the discrete spectrum case

Details Laplace and Schrödinger operators on regular metric trees: the discrete spectrum case Laplace and Schrödinger operators on regular metric trees: the discrete spectrum case

2001-11-02

arxiv.org/abs/math/0111023v1

in book: Function Spaces, Differential Operators and Nonlinear Amalysis, The Hans Triebel Anniversary Volume; D.Haroske, T.Run

Mathematics

Spectral Theory

20 pages

Scientific paper

The Schr\"odinger operator on a metric tree is a family of ordinary differential operators on its edges complemented by certain matching conditions at the vertices. The regular trees are highly symmetric. This allows one to construct an orthogonal decomposition of the space L_2 on the tree which reduces the Schr\"odinger operator with any symmetric weight. Using this decomposition, we analyse the spectrum of such operators, including the free Laplacian, under various assumptions about the tree and the potential.

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