The Gelfand transform of homogeneous distributions on Heisenberg type groups

Journal of the Australian Mathematical Society

Francesca Astengo¹ 

[1] Bianca Di Blasio

关键词: primary 43A80;    secondary 22E30;   

DOI  :  10.1017/S1446788700014336

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

A 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.

【 授权许可】

Unknown