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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Strichartz estimates for the Schrödinger equation for the sublaplacian on complex spheres
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by Valentina Casarino and Marco M. Peloso PDF
Trans. Amer. Math. Soc. 367 (2015), 2631-2664 Request permission

Abstract:

In this paper we consider the sublaplacian $\mathcal L$ on the unit complex sphere $S^{2n+1}\subset {\mathbf {C}}^{n+1}$, equipped with its natural CR structure, and derive Strichartz estimates with fractional loss of derivatives for the solutions of the free Schrödinger equation associated with $\mathcal L$. Our results are stated in terms of certain Sobolev-type spaces that measure the regularity of functions on $S^{2n+1}$ 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 ${\mathbf {N}}^2$.
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Additional Information
  • Valentina Casarino
  • Affiliation: DTG, Università degli Studi di Padova, Stradella san Nicola 3, I-36100 Vicenza, Italy
  • Email: valentina.casarino@unipd.it
  • Marco M. Peloso
  • Affiliation: Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, I-20133 Milano, Italy
  • Email: marco.peloso@unimi.it
  • Received by editor(s): January 25, 2013
  • Published electronically: July 24, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 2631-2664
  • MSC (2010): Primary 35Q41; Secondary 43A85, 35B65, 33C55
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06162-X
  • MathSciNet review: 3301876