Microlocal resolvent estimates, revisited

2016/02/10 by Shu Nakamura, Nakamura, Shu
Mathematics · #35A27 #35P25 #81U05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1602.03276

openalex publication_date 2016/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a Schrödinger type operator with long-range perturbation. We study the wave front set of the distribution kernel of (H-λ∓ i0)^-1, where λ is in the absolutely continous spectrumof H.The result is a refinement of the microlocal resolvent estimate of Isozaki-Kitada \citeIK1,IK2. We prove the result for a class of pseudodifferential operators on manifolds so that they apply to discrete Schrödinger operators and higher order operators on the Euclidean space. The proof relies on propagation estimates, whereas the original proof of Isozaki-Kitada relies on a construction of parametrices.

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