Corpus ID: 119132248

Frame sets for generalized $B$-splines

@article{Atindehou2018FrameSF,
  title={Frame sets for generalized \$B\$-splines},
  author={A. G. D. Atindehou and Yebeni B. Kouagou and K. Okoudjou},
  journal={arXiv: Functional Analysis},
  year={2018}
}
The frame set of a function $g\in L^2(\mathbb{R})$ is the subset of all parameters $(a, b)\in \mathbb{R}^2_+$ for which the time-frequency shifts of $g$ along $a\mathbb{Z}\times b\mathbb{Z}$ form a Gabor frame for $L^2(\mathbb{R}).$ In this paper, we investigate the frame set of a class of functions that we call \emph{generalized $B-$splines} and which includes the $B-$splines. In particular, we add many new points to the frame sets of these functions. In the process, we generalize and unify… Expand

Figures from this paper

On the frame set for the $2$-spline.
An invitation to Gabor analysis.

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