On the spectral theory of systems of first order equations with periodic distributional coefficients

2023/01/17 by Kevin Campbell, Campbell, Kevin, Rudi Weikard +1
Computer Science · Mathematics · #Advanced Topics in Algebra #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2301.07212

openalex publication_date 2023/01/17 · openalex created_date 2023/01/20 · openalex updated_date 2026/07/28

Abstract

We establish a Floquet theorem for a first-order system of differential equations u'=ru where r is an n× n-matrix whose entries are periodic distributions of order 0. Then we investigate, when n=1 and n=2, the spectral theory for the equation Ju'+qu=wf on \mathbb R when J is a real, constant, invertible, skew-symmetric matrix and q and w are periodic matrices whose entries are real distributions of order 0 with q symmetric and w non-negative.

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