Geodesic
Limiting Absorption Principle for Schrödinger Operators with Oscillating Potentials
Documenta mathematica, Tome 22 (2017), pp. 727-776
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Making use of the localised Putnam theory developed in [gj], we show the limiting absorption principle for Schrödinger operators with perturbed oscillating potential on appropriate energy intervals. We focus on a certain class of oscillating potentials (larger than the one in [GJ2]) that was already studied in [BD, DMR, DR1, DR2, MU, ReT1, ReT2]. Allowing long-range and short-range components and local singularities in the perturbation, we improve known results. A subclass of the considered potentials actually cannot be treated by the Mourre commutator method with the generator of dilations as conjugate operator. Inspired by [FH], we also show, in some cases, the absence of positive eigenvalues for our Schrödinger operators.
DOI : 10.4171/dm/577
Classification : 35J10
Mots-clés : Schrödinger operators, oscillating potentials, limiting absorption principle 
@article{10_4171_dm_577,
     author = {Thierry Jecko and Aiman Mbarek},
     title = {Limiting {Absorption} {Principle} for {Schr\"odinger} {Operators} with {Oscillating} {Potentials}},
     journal = {Documenta mathematica},
     pages = {727--776},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/577},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/577/}
}
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Thierry Jecko; Aiman Mbarek. Limiting Absorption Principle for Schrödinger Operators with Oscillating Potentials. Documenta mathematica, Tome 22 (2017), pp. 727-776. doi: 10.4171/dm/577

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