Year: 2013
Type: preprint
Abstract: Given a one-dimensional weighted Dirac operator we can define a spectral measure by virtue of singular Weyl-Titchmarsh-Kodaira theory. Using the theory of de Branges spaces we show that the spectral measure uniquely determines the Dirac operator up to a gauge transformation. Our result applies in particular to radial Dirac operators and extends the classical results for Dirac operators with one regular endpoint. Moreover, our result also improves the currently known results for canonical (Hamiltonian) systems. If one endpoint is limit circle case, we also establish corresponding two-spectra results.
Source: arXiv (Cornell University)
Institution: University of Vienna
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: AXA Research Fund, Austrian Science Fund
OpenAlex ID: W4296336900