2001/11/02 by Michael Solomyak
Mathematics · Physics and Astronomy · #math.SP #math-ph #math.MP #msc:34L40 #msc:47E05
published as in book: Function Spaces, Differential Operators and Nonlinear Amalysis, The Hans Triebel Anniversary Volume; D.Haroske, T.Runst, H.-J. Schmeisser (Ed.); Birkhäuser Verlag, 2003; pp. 161--181 · 20 pages
arxiv created 2001/11/02 · arxiv updated 2009/11/30
The Schrödinger 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 L2 on the tree which reduces the Schrödinger 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.