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Spectrum and Solutions of Dirac Systems
Author(s) -
Amar Emmanuelle
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200201)233:1<5::aid-mana5>3.0.co;2-m
Subject(s) - mathematics , characterization (materials science) , absolute continuity , spectrum (functional analysis) , continuous spectrum , pure mathematics , matrix (chemical analysis) , dirac (video compression format) , mathematical physics , quantum mechanics , materials science , physics , composite material , nanotechnology , neutrino
In this paper we consider the one‐dimensional Dirac systems on the semiaxis, whose potentials are continuous functions. We present two results concerning the spectral decomposition of such systems. First, we adapt the notion of subordinate solutions developed by D. Gilbert and D. Pearson for the Schrödinger equation, and we use an idea of Jitomirskaya‐Last , to establish a characterization of the spectrum in terms of the existence or non‐existence of subordinate solutions to the system. Then we exhibit a new characterization of the absolutely continuous spectrum, which relies on the transfer matrix.