Semiclassical resolvent estimates for short-range L∞ potentials. II

Article type: Research Article

Authors: Vodev, Georgi^{; *}

Affiliations: Université de Nantes, Laboratoire de Mathématiques Jean Leray, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 03, France. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We prove semiclassical resolvent estimates for real-valued potentials V∈L∞(Rn), n⩾3, of the form V=VL+VS, where VL is a long-range potential which is C1 with respect to the radial variable, while VS is a short-range potential satisfying VS(x)=O(⟨x⟩−δ) with δ>1.

Keywords: Schrödinger operator, resolvent estimates, short-range potentials

DOI: 10.3233/ASY-191562

Journal: Asymptotic Analysis, vol. 118, no. 4, pp. 297-312, 2020