论文标题
渐近估计组的松弛方程和较弱的规律性。
The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups
论文作者
论文摘要
我们在无限维谎言代数的背景下研究了宽松的方程。在顺序完整的渐近估计上下文中讨论了明确的解决方案，并得出了一个积分扩展（迭代的riemann积分的总和具有校正术语的嵌套换向器的总和）是因为lie代数是由米尔诺（Milnor）意义上的无限型二线lie lie组遗传的情况。在Banach Lie组（以及具有适当规律性属性的谎言组）的背景下，我们将Baker-Campbell-Dynkin-Hausdorff公式推广到乘积积分（在非Banach案中具有额外的Nilpotency假设）。我们将此公式与宽松方程获得的结果结合在一起，以根据指数图来得出产品积分的明确表示。非班纳克情况下的重要成分是我们引入的整体转换。这种转换图映射连续的谎言代数值曲线使曲线平滑并使产品整体不变。这种转换还用于证明在渐近估计环境中的规律性陈述。
We investigate the Lax equation in the context of infinite-dimensional Lie algebras. Explicit solutions are discussed in the sequentially complete asymptotic estimate context, and an integral expansion (sums of iterated Riemann integrals over nested commutators with correction term) is derived for the situation that the Lie algebra is inherited by an infinite-dimensional Lie group in Milnor's sense. In the context of Banach Lie groups (and Lie groups with suitable regularity properties), we generalize the Baker-Campbell-Dynkin-Hausdorff formula to the product integral (with additional nilpotency assumption in the non-Banach case). We combine this formula with the results obtained for the Lax equation to derive an explicit representation of the product integral in terms of the exponential map. An important ingredient in the non-Banach case is an integral transformation that we introduce. This transformation maps continuous Lie algebra-valued curves to smooth ones and leaves the product integral invariant. This transformation is also used to prove a regularity statement in the asymptotic estimate context.
