Scattering for the fractional magnetic Schrödinger operators

In this paper, we prove the existence of the scattering operator for the fractional magnetic Schrödinger operators. In order to do this, we construct the fractional distorted Fourier transforms with magnetic potentials. Applying the properties of the distorted Fourier transforms, the existence and t...

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Veröffentlicht in:Acta mathematica scientia 2024-11, Vol.44 (6), p.2391-2410
Hauptverfasser: Wei, Lei, Duan, Zhiwen
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, we prove the existence of the scattering operator for the fractional magnetic Schrödinger operators. In order to do this, we construct the fractional distorted Fourier transforms with magnetic potentials. Applying the properties of the distorted Fourier transforms, the existence and the asymptotic completeness of the wave operators are obtained. Furthermore, we prove the absence of positive eigenvalues for fractional magnetic Schrödinger operators.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-024-0618-9