Limiting absorption principle for discrete Schrödinger operators with a Wigner-von Neumann potential and a slowly decaying potential
Language
en
Article de revue
This item was published in
Annales Henri Poincaré. 2021-01, vol. 22, n° 1, p. 83-120
Springer Verlag
English Abstract
We consider discrete Schrödinger operators on ${\mathbb{Z}}^d$ for which the perturbation consists of the sum of a long-range type potential and a Wigner-von Neumann type potential. Still working in a framework of weighted ...Read more >
We consider discrete Schrödinger operators on ${\mathbb{Z}}^d$ for which the perturbation consists of the sum of a long-range type potential and a Wigner-von Neumann type potential. Still working in a framework of weighted Mourre theory, we improve the limiting absorption principle (LAP) that was obtained in [Ma1]. To our knowledge, this is a new result even in the one-dimensional case. The improvement consists in a weakening of the assumptions on the long-range potential and better LAP weights. The improvement relies only on the fact that the generator of dilations (which serves as conjugate operator) is bounded from above by the position operator. To exploit this, Loewner's theorem on operator monotone functions is invoked.Read less <
English Keywords
2010 Mathematics Subject Classification. 39A70
81Q10
47B25
47A10 limiting absorption principle
discrete Schrödinger operator
Wigner-von Neumann potential
Mourre theory
weighted Mourre theory
Loewner's theorem
polylogarithms
Origin
Hal imported