A Mourre estimate for a Schrodinger operator on a binary tree

被引：27

作者：

Allard, C ^{[1
]}

Froese, N ^{[1
]}

机构：

[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

来源：

REVIEWS IN MATHEMATICAL PHYSICS | 2000年 / 12卷 / 12期

关键词：

D O I：

10.1142/S0129055X00000575

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Let G be a binary tree with vertices V and H be a Schrodinger operator acting on l(2)(V). A decomposition of the space l(2)(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.

引用

页码：1655 / 1667

页数：13

共 7 条

[1] ALLARD C, 1997, THESIS U BRIT COLUMB
[2] Cycon H.L., 1987, TEXTS MONOGRAPHS PHY
[3] On the spectral properties of discrete Schrodinger operators
de Monvel, AB
Sahbani, J
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1998, 326 (09): : 1145 - 1150
[4] DEMONVEL AB, IN PRESS REV MATH PH
[5] SPECTRAL-ANALYSIS OF 2ND-ORDER ELLIPTIC-OPERATORS ON NONCOMPACT MANIFOLDS
FROESE, R
HISLOP, P
[J]. DUKE MATHEMATICAL JOURNAL, 1989, 58 (01) : 103 - 129
[6] GEORGESCU V, VIRIAL THEOREM QUANT
[7] Extended states in the Anderson model on the Bethe lattice
Klein, A
[J]. ADVANCES IN MATHEMATICS, 1998, 133 (01) : 163 - 184

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