A representation formula related to Schrodinger operators

2004/12/16 by Shijun Zheng, Zheng, Shijun
Computer Science · Mathematics · #35P25 #42C15 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.CA #math.SP #msc:35P25 #msc:42C15

paper · pdf · doi:10.48550/arxiv.math/0412314

four pages, to appear in Anal. Theo. Appl

arxiv created 2004/12/16 · openalex publication_date 2004/12/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a Schrodinger operator on the real line, where the potential is in L¹ and L². We define the perturbed Fourier transform F for H and show that F is an isometry from the absolute continuous subspace onto L². This property allows us to construct a kernel formula for spectral operators. The main theorem improves the author's previous result for certain short-range potentials.

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