Global transformations preserving Sturm–Liouville spectral data

H. Isozaki, E. L. Korotyaev

Research output

2 Citations (Scopus)

Abstract

We show the existence of a real analytic isomorphism between the space of the impedance function ρ of the Sturm–Liouville problem −ρ−22f′)′ +uf on (0, 1), where u is a function of ρ, ρ′, ρ″, and that of potential p of the Schrödinger equation −y″ +py on (0, 1), keeping their boundary conditions and spectral data. This mapping is associated with the classical Liouville transformation f → ρf, and yields a global isomorphism between solutions of inverse problems for the Sturm–Liouville equations of the impedance form and those of the Schrödinger equations.

Original languageEnglish
Pages (from-to)51-68
Number of pages18
JournalRussian Journal of Mathematical Physics
Volume24
Issue number1
DOIs
Publication statusPublished - 1 Jan 2017

Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'Global transformations preserving Sturm–Liouville spectral data'. Together they form a unique fingerprint.

  • Cite this