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Spherical Schrödinger Hamiltonians: Spectral Analysis and Time Decay

  • Luca FanelliEmail author
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Part of the Springer INdAM Series book series (SINDAMS, volume 18)

Abstract

In this survey, we review recent results concerning the canonical dispersive flow e itH led by a Schrödinger Hamiltonian H. We study, in particular, how the time decay of space L p -norms depends on the frequency localization of the initial datum with respect to the some suitable spherical expansion. A quite complete description of the phenomenon is given in terms of the eigenvalues and eigenfunctions of the restriction of H to the unit sphere, and a comparison with some uncertainty inequality is presented.

Keywords

Dispersive estimates Electromagnetic potentials Schrödinger equation 
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Notes

Acknowledgements

The author sincerely thanks all the organizers of the event Contemporary Trends in the Mathematics of Quantum Mechanics for the kind invitation, in particular Alessandro Michelangeli for his job. A special acknowledgement is to Prof. Gianfausto Dell’​Antonio, for his beautiful scientific contributions, for his teachings, and for his friendship.

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Dipartimento di MatematicaSAPIENZA Università di RomaRomaItaly

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