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Green's functions for first-order systems of ordinary differential equations without the unique continuation property
- Source :
- Integr. Equ. Oper. Theory 94 (2022)
- Publication Year :
- 2023
-
Abstract
- This paper is a contribution to the spectral theory associated with the differential equation $Ju'+qu=wf$ on the real interval $(a,b)$ when $J$ is a constant, invertible skew-Hermitian matrix and $q$ and $w$ are matrices whose entries are distributions of order zero with $q$ Hermitian and $w$ non-negative. Under these hypotheses it may not be possible to uniquely continue a solution from one point to another, thus blunting the standard tools of spectral theory. Despite this fact we are able to describe symmetric restrictions of the maximal relation associated with $Ju'+qu=wf$ and show the existence of Green's functions for self-adjoint relations even if unique continuation of solutions fails.
- Subjects :
- Mathematics - Spectral Theory
Mathematics - Classical Analysis and ODEs
Subjects
Details
- Database :
- arXiv
- Journal :
- Integr. Equ. Oper. Theory 94 (2022)
- Publication Type :
- Report
- Accession number :
- edsarx.2301.03521
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00020-022-02703-6