We prove that for every Lie group there exists a basis in its Lie algebra such that for each ¿=1 and each of its unitary representations. The separate and joint Gevrey vectors of order ¿ coincide. As a corollary we obtain that a vector is a Gevrey vector if, and only if, the corresponding positive definite function is a Gevrey function.
|Title of host publication||Circumspice: Various papers in and around mathematics in honor of Arnoud van Rooij|
|Place of Publication||Nijmegen|
|Publisher||Radboud Universiteit Nijmegen|
|Publication status||Published - 2001|