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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 $\theta:H\to {\rm Aut}(K)$ 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.
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참고문헌 (22)
참고문헌 신청
A. A. Arefijamaal / 2009 / On the square integrability of quasi regular representation on semidirect product groups / J. Geom. Anal 19 (3) : 541 ~ 552
A. A. Arefijamaal / 2010 / On construction of coherent states associated with homogeneous spaces / Turkish J. Math 34 (4) : 515 ~ 521
A. A. Arefijamaal / 2013 / Signal processing by alternate dual Gabor frames / Appl. Comput. Harmon. Anal 35 (3) : 535 ~ 540
A. A. Arefijamaal / 2013 / The continuous Zak transform and generalized Gabor frames / Mediterr. J. Math 10 (1) : 353 ~ 365
A. Ghaani Farashahi / 2013 / Convolution and involution on function spaces of homogeneous spaces / Bull. Malays. Math. Sci. Soc. (2) 36 (4) : 1109 ~ 1122
A. A. Arefijamaal / 2010 / On construction of coherent states associated with homogeneous spaces / Turkish J. Math 34 (4) : 515 ~ 521
A. A. Arefijamaal / 2013 / Signal processing by alternate dual Gabor frames / Appl. Comput. Harmon. Anal 35 (3) : 535 ~ 540
A. A. Arefijamaal / 2013 / The continuous Zak transform and generalized Gabor frames / Mediterr. J. Math 10 (1) : 353 ~ 365
A. Ghaani Farashahi / 2013 / Convolution and involution on function spaces of homogeneous spaces / Bull. Malays. Math. Sci. Soc. (2) 36 (4) : 1109 ~ 1122
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