In this paper we consider the sublaplacian L on the unit complex sphere S2n+1 subset of Cn+1, equipped with its natural CR structure, and derive Strichartz estimates with fractional loss of derivatives for the solutions of the free Schriidinger equation associated with L. Our results are stated in terms of certain Sobolev-type spaces that measure the regularity of functions on S2n+1 differently according to their spectral localization. Stronger conclusions are obtained for particular classes of solutions, corresponding to initial data whose spectrum is contained in a proper cone of N-2.

Strichartz estimates for the Schrödinger equation for the sublaplacian on complex spheres / V. Casarino, M.M. Peloso. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 367:4(2015 Apr 01), pp. PII S0002-9947(2014)06162-X.2631-PII S0002-9947(2014)06162-X.2664. [10.1090/S0002-9947-2014-06162-X]

Strichartz estimates for the Schrödinger equation for the sublaplacian on complex spheres

M.M. Peloso
2015

Abstract

In this paper we consider the sublaplacian L on the unit complex sphere S2n+1 subset of Cn+1, equipped with its natural CR structure, and derive Strichartz estimates with fractional loss of derivatives for the solutions of the free Schriidinger equation associated with L. Our results are stated in terms of certain Sobolev-type spaces that measure the regularity of functions on S2n+1 differently according to their spectral localization. Stronger conclusions are obtained for particular classes of solutions, corresponding to initial data whose spectrum is contained in a proper cone of N-2.
Schrodinger equation; Strichartz estimates; complex spheres; sublaplacian; dispersive estimates
Settore MAT/05 - Analisi Matematica
24-lug-2014
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/246763
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