Abstract relative Gabor transforms over canonical homogeneous spaces of semidirect product groups with Abelian normal factor

作者：Farashahi Arash Ghaani^*

来源：Analysis and Applications, 2017, 15(6): 795-813.

DOI：10.1142/S0219530517500075

• Canonical homogeneous space (left coset space)
• semi-direct product group
• dual group
• dual homogeneous space
• rho-function
• Gabor transform
• time-frequency analysis

This paper introduces a unified approach to the abstract notion of relative Gabor transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor. Let H be a locally compact group, K be a locally compact Abelian (LCA) group, and theta : H -> Aut(K) be a continuous homomorphism. Let G(theta) = H (sic)(theta) K be the semi-direct product of H and K with respect to theta, G(theta)/H be the canonical homogeneous space of G(theta), and mu(theta) be the canonical relatively invariant measure on G(theta)/H. Then we present a unified harmonic analysis approach to the theoretical aspects of the notion of relative Gabor transform over the Hilbert function space L-2 (G(theta)/H, mu(theta)).

• 出版日期2017-11