Sharp and plain estimates for Schrödinger perturbation of Gaussian kernel
We investigate whether a fundamental solution of the Schrödinger equation ∂ t u = (Δ + V ) u has local in time sharp Gaussian estimates. We compare that class with the class of V for which local in time plain Gaussian estimates hold. We concentrate on V that have fixed sign and we present certain co...
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| Veröffentlicht in: | Journal d'analyse mathématique (Jerusalem) 2024-04, Vol.152 (1), p.255-282 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We investigate whether a fundamental solution of the Schrödinger equation ∂
t
u
= (Δ +
V
)
u
has local in time sharp Gaussian estimates. We compare that class with the class of
V
for which local in time plain Gaussian estimates hold. We concentrate on
V
that have fixed sign and we present certain conclusions for
V
in the Kato class. |
|---|---|
| ISSN: | 0021-7670 1565-8538 |
| DOI: | 10.1007/s11854-023-0299-7 |