The $L^p$ boundedness of wave operators for Schrödinger operators with threshold singularities II. Even dimensional case
| dc.creator | Finco, Domenico | |
| dc.creator | Yajima, Kenji | |
| dc.date | 2006-05-10 | |
| dc.date.accessioned | 2026-07-07T07:13:44Z | |
| dc.date.available | 2026-07-07T07:13:44Z | |
| dc.description | In this paper we consider the wave operators $W_{\pm}$ for a Schrödinger operator $H$ in ${\bf{R}}^n$ with $n\geq 4$ even and we discuss the $L^p$ boundedness of $W_{\pm}$ assuming a suitable decay at infinity of the potential $V$. The analysis heavily depends on the singularities of the resolvent for small energy, that is if 0-energy eigenstates exist. If such eigenstates do not exist $W_{\pm}: L^p \to L^p$ are bounded for $1 \leq p \leq \infty$ otherwise this is true for $ \frac{n}{n-2} < p < \frac{n}{2} $. The extension to Sobolev space is discussed. | |
| dc.description | 59 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0605036 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0605036 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112581 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Spectral Theory | |
| dc.title | The $L^p$ boundedness of wave operators for Schrödinger operators with threshold singularities II. Even dimensional case | |
| dc.type | text |