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2019 | OriginalPaper | Buchkapitel

4. Gabor Frames: Characterizations and Coarse Structure

verfasst von : Karlheinz Gröchenig, Sarah Koppensteiner

Erschienen in: New Trends in Applied Harmonic Analysis, Volume 2

Verlag: Springer International Publishing

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Abstract

This chapter offers a systematic and streamlined exposition of the most important characterizations of Gabor frames over a lattice.

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Fußnoten
1
The terminology is often a bit different, e.g., [37] uses a “fiberization technique.”
 
2
It suffices to take the Fourier coefficients of the multivariate Fejer kernel \(\hat{F}_n(k) = \prod _{j=1}^d \big (1 - \frac{|k_j|}{n+1} \big )_{+}\) and set \(K_n (\nu ) = \hat{F}_n(A^T \nu ) = \hat{F}_n(k)\) for \(\nu = (A^T)^{-1}k \in \varLambda ^\perp \).
 
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Metadaten
Titel
Gabor Frames: Characterizations and Coarse Structure
verfasst von
Karlheinz Gröchenig
Sarah Koppensteiner
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-030-32353-0_4