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Asymptotic behavior of regularized scattering phases for long range perturbations

Jean-Marc Bouclet — 2002

Journées équations aux dérivées partielles

We define scattering phases for Schrödinger operators on ℝ d as limit of arguments of relative determinants. These phases can be defined for long range perturbations of the laplacian; therefore they can replace the spectral shift function (SSF) of Birman-Krein’s theory which can just be defined for some special short range perturbations (we shall recall this theory for non specialists). We prove the existence of asymptotic expansions for these phases, which generalize results on the SSF.

Littlewood-Paley decompositions on manifolds with ends

Jean-Marc Bouclet — 2010

Bulletin de la Société Mathématique de France

For certain non compact Riemannian manifolds with ends which may or may not satisfy the doubling condition on the volume of geodesic balls, we obtain Littlewood-Paley type estimates on (weighted) L p spaces, using the usual square function defined by a dyadic partition.

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