Harmonic analysis on heisenberg type groups from a geometric viewpoint

1984 ◽  
pp. 60-100 ◽  
Author(s):  
Michael Cowling ◽  
Adam Korányi
Keyword(s):  
Harmonic Analysis ◽  
Heisenberg Type ◽  
Heisenberg Type Groups

Marcinkiewicz multipliers and multi-parameter structure on Heisenberg (-type) groups, I

1995 ◽  
Vol 119 (1) ◽  
pp. 199-233 ◽  
Author(s):  
Detlef M�ller ◽  
Fulvio Ricci ◽  
Elias M. Stein
Keyword(s):  
Heisenberg Type ◽  
Heisenberg Type Groups ◽  
Marcinkiewicz Multipliers

Marcinkiewicz multipliers and multi-parameter structure on heisenberg (-type) groups, II

1996 ◽  
Vol 221 (1) ◽  
pp. 267-291 ◽  
Author(s):  
Detlef Müller ◽  
Fulvio Ricci ◽  
Elias M. Stein
Keyword(s):  
Heisenberg Type ◽  
Heisenberg Type Groups ◽  
Marcinkiewicz Multipliers

scholarly journals The Gelfand transform of homogeneous distributions on Heisenberg type groups

2006 ◽  
Vol 81 (3) ◽  
pp. 297-319
Author(s):  
Francesca Astengo ◽  
Bianca Di Blasio
Keyword(s):  
Heisenberg Group ◽  
Half Plane ◽  
Type Group ◽  
Gelfand Transform ◽  
Homogeneous Dimension ◽  
Heisenberg Type ◽  
Heisenberg Type Groups ◽  
Upper Half Plane ◽  
Homogeneous Distributions

AbstractA distribution on a Heisenberg type group of homogeneous dimension Q is a biradial kernel of type α if it coincides with a biradial function, homogeneous of degree α — Q, and smooth away from the identity. We prove that a distribution is a biradial kernel of type α, 0 < α < Q, if and only if its Gelfand transform, defined on the Heisenberg fan, extends to a smooth even function on the upper half plane, homogeneous of degree −α/2. A similar result holds for radial kernels on the Heisenberg group.

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