## Abstract

Let H be a separable Hilbert space with inner product (•,•). We say a set {f _{k}: k ∈ ℤ} is a (fundamental) frame for H if there exist A,B > 0 such that for each f ∈ H, A ∥ f ∥ ^{2} _{H} ≤ Σ _{n∈ℤ}|(f,f _{k})| ^{2}≤B∥f∥ ^{2} _{H} In case {f _{k}: k ∈ ℤ} is a frame for the subspace span{f _{k}: k ∈ ℤ}, we say that {f _{k}: k ∈ ℤ} is a frame sequence. A Weyl-Heisenberg frame sequence is a frame sequence which is generated by translated and modulated versions of L _{2}-functions. In this paper, we characterize Weyl-Heisenberg frame sequences using infinite Hermitian matrices and obtain the optimal frame bounds in terms of the operator norms of these matrices. This work is inspired by a paper by Casazza and Christensen, where sufficient conditions for a Weyl-Heisenberg system to be a frame sequence are studied.

Original language | English |
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Pages (from-to) | 385-401 |

Number of pages | 17 |

Journal | International Journal of Pure and Applied Mathematics |

Volume | 75 |

Issue number | 4 |

State | Published - 2012 |

## Keywords

- Frame sequences
- Hermitian matrix
- Modulation frames
- Weyl-Heisenberg systems

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