We consider 1-D Laplace operator with short range potential V (x) dacaying sufficiently rapidly. We study the equivalence of classical homogeneous Besov type spaces and the corresponding perturbed homogeneous Besov spaces associated with the perturbed Hamiltonian on the real line. It is shown that the ssumption zero is not a resonance guarantees that the perturbed and unperturbed homogeneous Besov norms are equivalent. As a corollary, the corresponding wave operators leave classical homogeneous Besov spaces invariant.
On homogeneous Besov spaces for 1D Hamiltonians without zero resonance
Gueorguiev, Vladimir Simeonov;Giammetta Anna Rita
2017-01-01
Abstract
We consider 1-D Laplace operator with short range potential V (x) dacaying sufficiently rapidly. We study the equivalence of classical homogeneous Besov type spaces and the corresponding perturbed homogeneous Besov spaces associated with the perturbed Hamiltonian on the real line. It is shown that the ssumption zero is not a resonance guarantees that the perturbed and unperturbed homogeneous Besov norms are equivalent. As a corollary, the corresponding wave operators leave classical homogeneous Besov spaces invariant.File in questo prodotto:
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