TY - JOUR

T1 - Global transformations preserving Sturm–Liouville spectral data

AU - Isozaki, H.

AU - Korotyaev, E. L.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We show the existence of a real analytic isomorphism between the space of the impedance function ρ of the Sturm–Liouville problem −ρ−2(ρ2f′)′ +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.

AB - We show the existence of a real analytic isomorphism between the space of the impedance function ρ of the Sturm–Liouville problem −ρ−2(ρ2f′)′ +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.

UR - http://www.scopus.com/inward/record.url?scp=85014764203&partnerID=8YFLogxK

U2 - 10.1134/S1061920817010046

DO - 10.1134/S1061920817010046

M3 - Article

AN - SCOPUS:85014764203

VL - 24

SP - 51

EP - 68

JO - Russian Journal of Mathematical Physics

JF - Russian Journal of Mathematical Physics

SN - 1061-9208

IS - 1

ER -