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TWISTED SHIFT-INVARIANT SYSTEM IN
$L^2(\mathbb {R}^{2N})$
- Part of
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- Journal:
- Nagoya Mathematical Journal / Volume 251 / September 2023
- Published online by Cambridge University Press:
- 05 June 2023, pp. 734-767
- Print publication:
- September 2023
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- Article
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- You have access
- Open access
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We consider a general twisted shift-invariant system,
$V^{t}(\mathcal {A})$, consisting of twisted translates of countably many generators and study the problem of obtaining a characterization for the system 
$V^{t}(\mathcal {A})$ to form a frame sequence or a Riesz sequence. We illustrate our theory with some examples. In addition to these results, we study a dual twisted shift-invariant system and also obtain an orthonormal sequence of twisted translates from a given Riesz sequence of twisted translates.
