2025/12/27 by Horia D. Cornean, Bernard Helffer, Cornean, Horia D. +3
Mathematics · #35S05 #43A70 #47G30 #81S99 #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics
paper · doi:10.48550/arxiv.2512.22547
openalex publication_date 2025/12/27 · openalex created_date 2025/12/31 · openalex updated_date 2026/07/28
We study the structure of the fibre operators corresponding to periodic magnetic pseudo-differential operators having periodic magnetic potentials. We obtain explicit formulas for their distribution kernel, both when these fibres are seen as operators on the d-dimensional torus, and also when they are seen as infinite matrices acting on a discrete ℓ2 space via a discrete Fourier transform. Moreover, using these distribution kernels we prove that the fibre operators are toroidal pseudo-differential operators.