Levene, R. H. and Power, Stephen C. (2010) *Manifolds of Hilbert Space Projections.* Proceedings of the London Mathematical Society, 100 (2). pp. 485-509. ISSN 1460-244X

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## Abstract

The Hardy space H2 () for the upper half-plane together with a multiplicative group of unimodular functions u() = exp(i(11 + ... +nn)), with n, gives rise to a manifold of orthogonal projections for the subspaces u() H2 () of L2 (). For classes of admissible functions i the strong operator topology closures of and are determined explicitly as various n-balls and n-spheres. The arguments used are direct and rely on the analysis of oscillatory integrals (E. M. STEIN, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series 43 (Princeton University Press, Princeton, NJ, 1993)) and Hilbert space geometry. Some classes of these closed projection manifolds are classified up to unitary equivalence. In particular, the Fourier–Plancherel 2-sphere and the hyperbolic 3-sphere of Katavolos and Power (A. KATAVOLOS and S. C. POWER, Translation and dilation invariant subspaces of L2(), J. reine angew. Math. 552 (2002) 101–129) appear as distinguished special cases admitting non-trivial unitary automorphism groups, which are explicitly described.

Item Type: | Article |
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Journal or Publication Title: | Proceedings of the London Mathematical Society |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 26716 |

Deposited By: | Professor Stephen C Power |

Deposited On: | 06 Jul 2009 09:18 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 27 Apr 2017 01:35 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/26716 |

### Available Versions of this Item

- Manifolds of Hilbert Space Projections. (deposited 07 Feb 2008 10:19)
- Manifolds of Hilbert Space Projections. (deposited 06 Jul 2009 09:18)
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- Manifolds of Hilbert Space Projections. (deposited 06 Jul 2009 09:18)

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