solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看13127次
Differentiability of the Evolution Map and Mackey Continuity. (arXiv:1812.08777v1 [math.FA])
来源于:arXiv
We solve the differentiablity problem for the evolution map in Milnor's
infinite dimensional setting. We first show that the evolution map of each
$C^k$-semiregular Lie group admits a particular kind of sequentially continuity
$-$ called Mackey continuity $-$ and then prove that this continuity property
is strong enough to ensure differentiability of the evolution map. In
particular, this drops any continuity presumptions made in this context so far.
Remarkably, Mackey continuity rises directly from the regularity problem itself
$-$ which makes it particular among the continuity conditions traditionally
considered. As a further application of the introduced notions, we discuss the
strong Trotter property in the sequentially-, and the Mackey continuous
context. 查看全文>>