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

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dc.creatorSolomyak, Michael
dc.date2001-11-02
dc.date.accessioned2026-07-07T04:44:13Z
dc.date.available2026-07-07T04:44:13Z
dc.descriptionThe 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 L_2 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.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0111023
dc.identifierhttp://arxiv.org/abs/math/0111023
dc.identifierin 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
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62549
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subject34L40 (Primary) 47E05 (Secondary)
dc.titleLaplace and Schrödinger operators on regular metric trees: the discrete spectrum case
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