论文标题
到“无相空间中心歧管”的折面
Corrigendum to "Center Manifolds without a Phase Space"
论文作者
论文摘要
在[G. Faye和A. Scheel，\ textit {trans。阿米尔。数学。 Soc。}，370（2018），第5843---5885页。其中的主要结果建立了通过卷积算子通过非本地耦合在实际线上构成的非线性功能方程系统的中心歧管。在构造中，我们需要修改非线性，以使其映射成指数增长的功能的空间，并拥有一个小的Lipschitz常数。呈现的截止功能适用于基于$ l^\ infty $的结构，但不足以选择$ h^1 $ - 空格。我们纠正此选择，并证明对置于叠加非线性的影响。
We correct the choice of cut-off function in our construction of center manifolds in [G. Faye and A. Scheel, \textit{Trans. Amer. Math. Soc.}, 370 (2018), pp. 5843--5885]. The main result there establishes center manifolds for systems of nonlinear functional equations posed on the real line with nonlocal coupling through convolution operators. In the construction, we need to modify the nonlinearity such that it maps spaces of exponentially growing functions into itself and possesses a small Lipschitz constant. The cut-off function presented there is suitable for $L^\infty$-based construction but insufficient for the choice of $H^1$-spaces. We correct this choice and demonstrate the effect on a pointwise superposition nonlinearity.
