Gabor analysis for a broad class of quasi-Banach modulation spaces

Joachim Toft

Gabor analysis for a broad class of quasi-Banach modulation spaces

Functional Analysis 2014-09-09 v3

Authors: Joachim Toft

Abstract

We extend the Gabor analysis in \cite{GaSa} to a broad class of modulation spaces, allowing more general mixed quasi-norm estimates and weights in the definition of the modulation space quasi-norm. For such spaces we deduce invariance and embedding properties, and that the elements admit reconstructible sequence space representations using Gabor frames.

Keywords

gabor analysis modulation spaces quasi-banach spaces mixed quasi-norm estimates weights gabor frames sequence space representations

Cite

@article{arxiv.1404.0758,
  title  = {Gabor analysis for a broad class of quasi-Banach modulation spaces},
  author = {Joachim Toft},
  journal= {arXiv preprint arXiv:1404.0758},
  year   = {2014}
}

Comments

32 pages. Certain identification results on Fourier Lebesgue and modulation spaces for compactly supported elements is added in the second version. A thorough revision is done in this third version of the paper. arXiv admin note: text overlap with arXiv:1406.3820

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