# Generalized Weyl–Heisenberg (GWH) groups

Generalized Weyl–Heisenberg (GWH) groups Let $$H$$ H be a locally compact group, $$K$$ K be a locally compact Abelian (LCA) group, $$\theta :H\rightarrow Aut(K)$$ θ : H → A u t ( K ) be a continuous homomorphism, and let $$G_\theta =H\ltimes _\theta K$$ G θ = H ⋉ θ K be the semi-direct product of $$H$$ H and $$K$$ K with respect to the continuous homomorphism $$\theta$$ θ . In this article, we introduce the Generalized Weyl–Heisenberg (GWH) group $${\mathbb {H}}(G_\theta )$$ H ( G θ ) associate with the semi-direct product group $$G_\theta$$ G θ . We will study basic properties of $${\mathbb {H}}(G_\theta )$$ H ( G θ ) from harmonic analysis aspects. Finally, we will illustrate applications of these methods in the case of some well-known semi-direct product groups. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# Generalized Weyl–Heisenberg (GWH) groups

, Volume 4 (3) – Nov 17, 2013
11 pages

/lp/springer-journals/generalized-weyl-heisenberg-gwh-groups-gzNBE20M6S
Publisher
Springer Journals
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-013-0065-6
Publisher site
See Article on Publisher Site

### Abstract

Let $$H$$ H be a locally compact group, $$K$$ K be a locally compact Abelian (LCA) group, $$\theta :H\rightarrow Aut(K)$$ θ : H → A u t ( K ) be a continuous homomorphism, and let $$G_\theta =H\ltimes _\theta K$$ G θ = H ⋉ θ K be the semi-direct product of $$H$$ H and $$K$$ K with respect to the continuous homomorphism $$\theta$$ θ . In this article, we introduce the Generalized Weyl–Heisenberg (GWH) group $${\mathbb {H}}(G_\theta )$$ H ( G θ ) associate with the semi-direct product group $$G_\theta$$ G θ . We will study basic properties of $${\mathbb {H}}(G_\theta )$$ H ( G θ ) from harmonic analysis aspects. Finally, we will illustrate applications of these methods in the case of some well-known semi-direct product groups.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Nov 17, 2013