A non-overdetermined inverse problem of finding the potential from the spectral function
| dc.creator | Ramm, A. G. | |
| dc.date | 2000-11-20 | |
| dc.date | 2001-03-28 | |
| dc.date.accessioned | 2026-07-07T04:28:08Z | |
| dc.date.available | 2026-07-07T04:28:08Z | |
| dc.description | Let $D\subset \R^n$, $n\geq 3,$ be a bounded domain with a $C^{\infty}$ boundary $S$, $L=-\nabla^2+q(x)$ be a selfadjoint operator defined in $H=L^2(D)$ by the Neumann boundary condition, $θ(x,y,λ)$ be its spectral function, $θ(x,y,λ):=\ds\sum_{λ_j<λ} ϕ_j(x)ϕ$ where $Lϕ_j=λ_jϕ_j$, $ϕ_{j N}|_S=0,$ $\|ϕ_j\|_{L^2(D)}=1$, $j=1,2,...$. The potential $q(x)$ is a real-valued function, $q\in C^\infty(D)$. It is proved that $q(x)$ is uniquely determined by the data $θ(s,s,λ) \forall s\in S$, $\forall λ\in \R_+$ if all the eigenvalues of $L$ are simple. | |
| dc.description | 14pp | |
| dc.identifier | https://arxiv.org/abs/math-ph/0011035 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0011035 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56671 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35R30 | |
| dc.title | A non-overdetermined inverse problem of finding the potential from the spectral function | |
| dc.type | text |