Reconstruction of the potential from I-function
| dc.creator | Ramm, A. G. | |
| dc.date | 2001-02-22 | |
| dc.date | 2001-03-31 | |
| dc.date.accessioned | 2026-07-07T04:28:19Z | |
| dc.date.available | 2026-07-07T04:28:19Z | |
| dc.description | If $f(x,k)$ is the Jost solution and $f(x) = f(0,k)$, then the $I$-function is $I(k) := \frac{f^\prime(0,k)}{f(k)}$. It is proved that $I(k)$ is in one-to-one correspondence with the scattering triple ${\mathcal S} :=\{S(k), k_j, s_j, \quad 1 \leq j \leq J\}$ and with the spectral function $ρ(λ)$ of the Sturm-Liouville operator $l= -\frac{d^2}{dx^2} + q(x)$ on $(0, \infty)$ with the Dirichlet condition at $x=0$ and $q(x) \in L_{1,1} := \{q: q= \bar q, \int^\infty_0 (1+x) |q(x) dx < \infty\}$. Analytical methods are given for finding $\mathcal S$ from $I(k)$ and $I(k)$ from $\mathcal S$, and $ρ(λ)$ from $I(k)$ and $I(k)$ from $ρ(λ)$. Since the methods for finding $q(x)$ from $\mathcal S$ or from $ρ(λ)$ are known, this yields the methods for finding $q(x)$ from $I(k)$. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0102028 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0102028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56742 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 34R30 | |
| dc.title | Reconstruction of the potential from I-function | |
| dc.type | text |