Geodesic
Limiting Absorption Principle for Schrödinger Operators with Oscillating Potentials
Documenta mathematica, Tome 22 (2017), pp. 727-776.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 35J10
Keywords: Schrödinger operators, oscillating potentials, limiting absorption principle 
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     author = {Jecko, Thierry and Mbarek, Aiman},
     title = {Limiting {Absorption} {Principle} for {Schr\"odinger} {Operators} with {Oscillating} {Potentials}},
     journal = {Documenta mathematica},
     pages = {727--776},
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     volume = {22},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a32/}
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Jecko, Thierry; Mbarek, Aiman. Limiting Absorption Principle for Schrödinger Operators with Oscillating Potentials. Documenta mathematica, Tome 22 (2017), pp. 727-776. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a32/