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The Marchenko–Ostrovski mapping and the trace formula for the Camassa–Holm equation
- Source :
-
Journal of Functional Analysis . Oct2003, Vol. 203 Issue 2, p494. 25p. - Publication Year :
- 2003
-
Abstract
- We consider the periodic weighted operator <f>Ty=−ρ−2(ρ2y′)′+<NU>1</NU>/4 ρ−4</f> in <f>L2(R,ρ2 dx)</f> where <f>ρ</f> is a 1-periodic positive function satisfying <f>q=ρ′/ρ∈L2(0,1)</f>. The spectrum of <f>T</f> consists of intervals separated by gaps. In the first part of the paper we construct the Marchenko–Ostrovski mapping <f>q→h(q)</f> and solve the corresponding inverse problem. For our approach it is essential that the mapping <f>h</f> has the factorization <f>h(q)=h0(V(q))</f>, where <f>q→V(q)</f> is a certain nonlinear mapping and <f>V→h0(V)</f> 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 <f>T</f>. [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICAL mappings
*TOPOLOGY
*MATHEMATICAL transformations
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 203
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 10741072
- Full Text :
- https://doi.org/10.1016/S0022-1236(03)00058-2