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Article Dans Une Revue Annales Henri Poincaré Année : 2020

SEMI-CLASSICAL RESOLVENT ESTIMATES FOR L ∞ POTENTIALS ON RIEMANNIAN MANIFOLDS

Georgi Vodev
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Résumé

We prove semi-classical resolvent estimates for the Schrödinger operator with a real-valued L ∞ potential on non-compact, connected Riemannian manifolds which may have a compact smooth boundary. We show that the resolvent bound depends on the structure of the man-ifold at infinity. In particular, we show that for compactly supported real-valued L ∞ potentials and asymptoticaly Euclidean manifolds the resolvent bound is of the form exp(Ch −4/3 log(h −1)), while for asymptoticaly hyperbolic manifolds it is of the form exp(Ch −4/3), where C > 0 is some constant.
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Dates et versions

hal-02057007 , version 1 (05-03-2019)
hal-02057007 , version 2 (21-03-2019)

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Citer

Georgi Vodev. SEMI-CLASSICAL RESOLVENT ESTIMATES FOR L ∞ POTENTIALS ON RIEMANNIAN MANIFOLDS. Annales Henri Poincaré, 2020, 21 (2), pp.437-459. ⟨hal-02057007v2⟩
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