The limit-point/limit-circle classification for ordinary differential equations with distributional coefficients

2023/09/10 by Varun Bhardwaj, Bhardwaj, Varun, Rudi Weikard +1
Mathematics · Physics and Astronomy · #34B20 (Primary) 34L05 #47B25 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods for differential equations #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2309.05068

openalex publication_date 2023/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the limit-point/limit-circle classification for the differential equation Ju'+qu=λwu where J=(\beginsmallmatrix0&-1 1&0\endsmallmatrix) and q and w are matrices whose entries are distributions of order zero with q Hermitian and w non-negative. We identify the situations when the classical alternative of Weyl works and when it fails.

Related

• Limiting spectral distribution of Toeplitz and Hankel matrices with dependent entries
• Almost-Hermitian random matrices and bandlimited point processes
• On Local laws for non-Hermitian random matrices and their products
• Painleve formulas of the limiting distributions for non-null complex sample covariance matrices
• Loi de Weyl presque sure pour un systeme differentiel en dimension 1