ABSTRACT HARMONIC ANALYSIS OF RELATIVE CONVOLUTIONS OVER CANONICAL HOMOGENEOUS SPACES OF SEMIDIRECT PRODUCT GROUPS
2016 ◽
Vol 101
(2)
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pp. 171-187
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Keyword(s):
This paper presents a structured study for abstract harmonic analysis of relative convolutions over canonical homogeneous spaces of semidirect product groups. Let $H,K$ be locally compact groups and $\unicode[STIX]{x1D703}:H\rightarrow \text{Aut}(K)$ be a continuous homomorphism. Let $G_{\unicode[STIX]{x1D703}}=H\ltimes _{\unicode[STIX]{x1D703}}K$ be the semidirect product of $H$ and $K$ with respect to $\unicode[STIX]{x1D703}$ and $G_{\unicode[STIX]{x1D703}}/H$ be the canonical homogeneous space (left coset space) of $G_{\unicode[STIX]{x1D703}}/H$. We present a unified approach to the harmonic analysis of relative convolutions over the canonical homogeneous space $G_{\unicode[STIX]{x1D703}}/H$.
2018 ◽
Vol 29
(01)
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pp. 1850005
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Keyword(s):
2017 ◽
Vol 15
(06)
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pp. 795-813
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2017 ◽
Vol 60
(1)
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pp. 111-121
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Keyword(s):
1981 ◽
Vol 33
(5)
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pp. 1097-1110
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Keyword(s):
2018 ◽
Vol 70
(1)
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pp. 97-116
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2008 ◽
Vol 06
(05)
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pp. 749-759
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2005 ◽
Vol 16
(09)
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pp. 941-955
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Keyword(s):
Keyword(s):
2013 ◽
Vol 56
(1)
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pp. 218-224
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