Another Application of Dilation Analytic Method for Complex\n Lieb--Thirring Type Estimates

2020/02/26 by Norihiro Someyama, Someyama, Norihiro
Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2003.09238

openalex publication_date 2020/02/26 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We consider non-self-adjoint Schr "odinger operators H_ rm\nc=-\Δ+V_ rm c (resp. H_ rm r=-\Δ+V_ rm r) acting in\nL²( mathbb R^d), d\≥ 1, with dilation analytic complex (resp. real)\npotentials. We were able to find out perhaps a new application of dilation\nanalytic method in citeSo1 (N. Someyama, "Number of Eigenvalues of\nNon-self-adjoint Schr "odinger Operators with Dilation Analytic Complex\nPotentials," Reports on Mathematical Physics, Volume 83, Issue 2, pp.163-174\n(2019).). We give a Lieb--Thirring type estimate on resonance eigenvalues of\nH_ rm c in the open complex sector and that on embedded eigenvalues of\nH_ rm r in the same way as citeSo1. To achieve that, we derive\nLieb--Thirring type inequalities for isolated eigenvalues of H on several\ncomplex subplanes.\n

Citations

• A class of analytic perturbations for one-body Schrödinger Hamiltonians

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