Frames and their associated $\emph{H}_{{\kern-2pt}\emph{F}}^{\emph{p}}$-subspaces

  • Authors:

  • Deguang Han;Pengtong Li;Wai-Shing Tang

  • Affiliations:

  • Department of Mathematics, University of Central Florida, Orlando, USA 32816;Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China 210016;Department of Mathematics, National University of Singapore, Singapore, Republic of Singapore 119076

  • Venue:
  • Advances in Computational Mathematics
  • Year:
  • 2011

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Abstract

Given a frame F驴=驴{f j } for a separable Hilbert space H, we introduce the linear subspace $H^{p}_{F}$ of H consisting of elements whose frame coefficient sequences belong to the 驴 p -space, where 1驴驴驴p驴p-frames, realizations and dilations. In particular we show that for closed linear subspaces of H, only finite dimensional ones can be realized as $H^{p}_{F}$ -spaces for some frame F. We also prove that with a mild decay condition on the frame F the frame expansion of any element in $H_{F}^{p}$ converges in both the Hilbert space norm and the ||·|| F, p -norm which is induced by the 驴 p -norm.