Abstract
Let \(H\) be a locally compact group, \(K\) be a locally compact Abelian (LCA) group, \(\theta :H\rightarrow Aut(K)\) be a continuous homomorphism, and let \(G_\theta =H\ltimes _\theta K\) be the semi-direct product of \(H\) and \(K\) with respect to the continuous homomorphism \(\theta \). In this article, we introduce the Generalized Weyl–Heisenberg (GWH) group \({\mathbb {H}}(G_\theta )\) associate with the semi-direct product group \(G_\theta \). We will study basic properties of \({\mathbb {H}}(G_\theta )\) from harmonic analysis aspects. Finally, we will illustrate applications of these methods in the case of some well-known semi-direct product groups.
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Ghaani Farashahi, A. Generalized Weyl–Heisenberg (GWH) groups. Anal.Math.Phys. 4, 187–197 (2014). https://doi.org/10.1007/s13324-013-0065-6
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DOI: https://doi.org/10.1007/s13324-013-0065-6
Keywords
- Wavelet analysis
- Gabor analysis
- Semi-direct product
- Locally compact group
- Locally compact Abelian (LCA) group
- Weyl–Heisenberg (WH) group
- Generalized Weyl–Heisenberg (GWH) group