Resonances and lower resolvent bounds

DOI10.4171/JST/108zbMath1326.35299arXiv1402.0604MaRDI QIDQ748370

Maciej Zworski, Kiril Datchev, Semyon Dyatlov

Publication date: 20 October 2015

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.0604

zbMATH Keywords

resolvent estimatessemiclassical analysisscattering resonances

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) PDEs in connection with quantum mechanics (35Q40)

Related Items (13)

A bound for the eigenvalue counting function for Krein-von Neumann and Friedrichs extensions ⋮ Semiclassical estimates for scattering on the real line ⋮ Exponential lower resolvent bounds far away from trapped sets ⋮ Semiclassical resolvent bound for compactly supporte \(L^\infty\) potentials ⋮ Semiclassical resolvent bounds for short range L ∞ potentials with singularities at the origin ⋮ Semiclassical resolvent bounds for compactly supported radial potentials ⋮ The Scattering Resonances for Schrödinger-Type Operators with Unbounded Potentials ⋮ Improved resolvent bounds for radial potentials ⋮ Semiclassical resolvent bounds in dimension two ⋮ Mathematical study of scattering resonances ⋮ Semiclassical resolvent estimates for short-range \(L^\infty\) potentials ⋮ Semiclassical resolvent estimates for \(L^\infty\) potentials on Riemannian manifolds ⋮ Applications of resonance theory without analyticity assumption

Cites Work

• Microlocalization of resonant states and estimates of the residue of the scattering amplitude
• Lower bounds for shape resonances widths of long range Schrodinger operators
• Geometric control in the presence of a black box

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