Year: 2013
Type: preprint
Abstract: We show the existence of a real analytic isomorphism between a space of impedance function $ρ$ of the Sturm-Liouville problem $- ρ^{-2}(ρ^2f')' + uf$ on $(0,1)$, where $u$ is a function of $ρ, ρ', ρ''$, and that of potential $p$ of the Schr{ö}dinger equation $- y'' + py$ on $(0,1)$, keeping their boundary conditions and spectral data. This mapping is associated with the classical Liouville transformation $f \to ρf$, and yields a global isomorphism between solutions to inverse problems for the Sturm-Liouville equations of the impedance form and those to the Schr{ö}dinger equations.
Source: arXiv (Cornell University)
Authors: Isozaki, Hiroshi, Korotyaev, Evgeny L.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1952859387