H-type groups and Iwasawa decompositions

Cowling, Michael; Dooley, A. H.; Korányi, Adam; Ricci, Fulvio

doi:10.1016/0001-8708(91)90060-k

Cited by 167 publications

(187 citation statements)

References 18 publications

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“…Groups of H-type were introduced by Kaplan in 7 as direct generalizations of Heisenberg groups, and they have been studied quite extensively; see [16][17][18][19] and the references therein.…”

Section: Rellich Inequality On H-type Groupsmentioning

confidence: 99%

Weighted Rellich Inequality on H-Type Groups and Nonisotropic Heisenberg Groups

Jin

Han

2010

J Inequal Appl

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Section: Rellich Inequality On H-type Groupsmentioning

confidence: 99%

Weighted Rellich Inequality on H-Type Groups and Nonisotropic Heisenberg Groups

Jin

Han

2010

J Inequal Appl

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“…See [11] (page 146). For further references, see [2,3]. In summary, the action of an isometry on the ideal boundary of rank one symmetric space, which fixes 0 and ∞, is of the form…”

Section: Theorem 1 Let γ ⊂ G Be a Nonelementary Nonparabolic Group Imentioning

confidence: 99%

Length spectrum in rank one symmetric space is not arithmetic

Ким

2006

Proc. Amer. Math. Soc.

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“…where c is a constant depending only on m and k and It is known that if n = 0 © 3 and n' = t>' 0 3' are H-type algebra such that dimn = dimn' and dim 3 = dim 3' then n and n' are not necessarily isomorphic (see [5]); however, the associated hypergroups are isomorphic. THEOREM 2.3.…”

Section: Theorem 21 the Locally Compact Space X Is A Hypergroup Witmentioning

confidence: 99%

Hypergroups associated to harmonic NA groups

Blasio

2002

J. Aust. Math. Soc.

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A harmonic NA group is a suitable solvable extension of a two-step nilpotent Lie group N of Heisenberg type by R + , which acts on N by anisotropic dilations. A hypergroup is a locally compact space for which the space of Borel measures has a convolution structure preserving the probability measures and satisfying suitable conditions. We describe a class of hypergroups associated to NA groups.2000 Mathematics subject classification: primary 43A62,43A80.

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H-type groups and Iwasawa decompositions

Cited by 167 publications

References 18 publications

Weighted Rellich Inequality on H-Type Groups and Nonisotropic Heisenberg Groups

Weighted Rellich Inequality on H-Type Groups and Nonisotropic Heisenberg Groups

Length spectrum in rank one symmetric space is not arithmetic

Hypergroups associated to harmonic NA groups

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