## Abstract

We present a characterization of the modulation space S_{o} in terms of the Zak transform of its elements. We illustrate our result by considering S^{-λ}h, where h is the standard Gaussian, S is the "frame" operator corresponding to the critical-density Gabor system (h, a = 1, b = 1), and λ ∈ [0,3/2). Both the proof of the main result and the example require basics from Gabor frame theory; these are developed in a separate section. We further use a result from recent work by Gröchenig and Leinert on Wiener-type theorems in a non-commutative setting. We also present an extension of our main result to more general modulation spaces.

Original language | English |
---|---|

Pages (from-to) | 141-162 |

Number of pages | 22 |

Journal | Sampling Theory in Signal and Image Processing |

Volume | 5 |

Issue number | 2 |

Publication status | Published - 1 May 2006 |

Externally published | Yes |

## Keywords

- Critical density
- Feichtinger space S
- Gabor system
- Modulation space
- Sampled short-time Fourier transform
- Zak transform

## Fingerprint

Dive into the research topics of 'Zak transform characterization of S_{0}'. Together they form a unique fingerprint.