Agmon-kato-kuroda theorems for a large class of perturbations

Alexandru D. Ionescu, Wilhelm Schlag

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

We prove asymptotic completeness for operators of the form H = -Δ + L on L2(ℝd), d ≥ 2, where L is an admissible perturbation. Our class of admissible perturbations contains multiplication operators defined by real-valued potentials V ∈ Lq(ℝ d), q ∈ [d/2, (d + 1)/2] (if d = 2, then we require q ∈ (1, 3/2]), as well as real-valued potentials V satisfying a global Kato condition. The class of admissible perturbations also contains first-order differential operators of the form a · ∇ - ∇ · a for suitable vector potentials a. Our main technical statement is a new limiting absorption principle, which we prove using techniques from harmonic analysis related to the Stein-Tomas restriction theorem.

Original languageEnglish (US)
Pages (from-to)397-440
Number of pages44
JournalDuke Mathematical Journal
Volume131
Issue number3
DOIs
StatePublished - Feb 15 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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