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http://dx.doi.org/10.4134/JKMS.j150610

ABSTRACT RELATIVE FOURIER TRANSFORMS OVER CANONICAL HOMOGENEOUS SPACES OF SEMI-DIRECT PRODUCT GROUPS WITH ABELIAN NORMAL FACTOR  

Farashahi, Arash Ghaani (Numerical Harmonic Analysis Group (NuHAG) Faculty of Mathematics University of Vienna)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.1, 2017 , pp. 117-139 More about this Journal
Abstract
This paper presents a systematic study for theoretical aspects of a unified approach to the abstract relative Fourier 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 ${\theta}:H{\rightarrow}Aut(K)$ be a continuous homomorphism. Let $G_{\theta}=H{\ltimes}_{\theta}K$ be the semi-direct product of H and K with respect to ${\theta}$ and $G_{\theta}/H$ be the canonical homogeneous space (left coset space) of $G_{\theta}$. We introduce the notions of relative dual homogeneous space and also abstract relative Fourier transform over $G_{\theta}/H$. Then we study theoretical properties of this approach.
Keywords
canonical homogeneous space; dual homogeneous space; relative convolution; relative Fourier transform; Plancherel formula; semi-direct product groups;
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