Academic Journal
$L^p$-continuity of wave operators for higher order Schrödinger operators with threshold eigenvalues in high dimensions: \(L^p\)-continuity of wave operators for higher order Schrödinger operators with threshold eigenvalues in high dimensions
| Τίτλος: | $L^p$-continuity of wave operators for higher order Schrödinger operators with threshold eigenvalues in high dimensions: \(L^p\)-continuity of wave operators for higher order Schrödinger operators with threshold eigenvalues in high dimensions |
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| Συγγραφείς: | Erdoğan, M. Burak, Green, William R., LaMaster, Kevin |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | arXiv, 2024. |
| Έτος έκδοσης: | 2024 |
| Θεματικοί όροι: | Scattering theory of linear operators, wave operators, \(L^p\)-continuity, FOS: Physical sciences, Mathematical Physics (math-ph), \(L^p\)-boundedness, higher order Schrödinger, Higher-order elliptic equations, Mathematics - Analysis of PDEs, FOS: Mathematics, eigenvalue, Mathematical Physics, Selfadjoint operator theory in quantum theory, including spectral analysis, Analysis of PDEs (math.AP) |
| Περιγραφή: | We consider the higher order Schrödinger operator $H=(-Δ)^m+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>4m$, $m\in \mathbb N$. We adapt our recent results for $m>1$ to show that when $H$ has a threshold eigenvalue the wave operators are bounded on $L^p(\mathbb R^n)$ for the natural range $1\leq p Updated to reflect referee comments, to appear in Discrete and Continuous Dynamical Systems. arXiv admin note: text overlap with arXiv:2207.14264 |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/xml |
| DOI: | 10.48550/arxiv.2407.07069 |
| DOI: | 10.3934/dcds.2025019 |
| Σύνδεσμος πρόσβασης: | http://arxiv.org/abs/2407.07069 |
| Rights: | CC BY |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....621a6bdcfe2b53aa6e9ba79a6d636e0f |
| Βάση Δεδομένων: | OpenAIRE |
| DOI: | 10.48550/arxiv.2407.07069 |
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