TY - JOUR

T1 - The Marchenko–Ostrovski mapping and the trace formula for the Camassa–Holm equation

AU - Badanin, Andrei

AU - Klein, Markus

AU - Коротяев, Евгений Леонидович

PY - 2003

Y1 - 2003

N2 - We consider the periodic weighted operator Ty=−ρ−2(ρ2y′)′+14ρ−4 in L2(R,ρ2dx) where ρ is a 1-periodic positive function satisfying q=ρ′/ρ∈L2(0,1). The spectrum of T consists of intervals separated by gaps. In the first part of the paper we construct the Marchenko–Ostrovski mapping q→h(q) and solve the corresponding inverse problem. For our approach it is essential that the mapping h has the factorization h(q)=h0(V(q)), where q→V(q) is a certain nonlinear mapping and V→h0(V) is the Marchenko–Ostrovski mapping for the Hill operator. Moreover, we solve the inverse problem for the gap length mapping. In the second part of this paper we derive the trace formula for T.

AB - We consider the periodic weighted operator Ty=−ρ−2(ρ2y′)′+14ρ−4 in L2(R,ρ2dx) where ρ is a 1-periodic positive function satisfying q=ρ′/ρ∈L2(0,1). The spectrum of T consists of intervals separated by gaps. In the first part of the paper we construct the Marchenko–Ostrovski mapping q→h(q) and solve the corresponding inverse problem. For our approach it is essential that the mapping h has the factorization h(q)=h0(V(q)), where q→V(q) is a certain nonlinear mapping and V→h0(V) is the Marchenko–Ostrovski mapping for the Hill operator. Moreover, we solve the inverse problem for the gap length mapping. In the second part of this paper we derive the trace formula for T.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-0141614994&origin=inward&txGid=7b46228eb9ff21ffa108de66766893eb

U2 - 10.1016/S0022-1236(03)00058-2

DO - 10.1016/S0022-1236(03)00058-2

M3 - статья

VL - 203

SP - 494

EP - 518

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 2

ER -