2020/02/29 by Sylvain Golénia, Sylvain Golenia, Marc-Adrien Mandich
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Limiting #Logarithm #Numerical methods in inverse problems #Operator (biology) #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Potential theory #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications #math-ph #math.FA #math.MP #math.SP
paper · pdf · doi:10.1007/s00023-020-00971-9
published as Annales Henri Poincar{é}, Springer Verlag, 2021, 22 (1), pp.83-120
openalex created_date 2020/02/24 · openalex publication_date 2020/10/20 · arxiv created 2021/01/22 · arxiv updated 2021/01/25 · openalex updated_date 2026/08/05
We consider discrete Schrödinger operators on ℤd 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.