We construct stable invariant manifolds for a large class of nonautonomous delay difference equations with infinite delay. This requires considering an appropriate class of phase spaces that are Banach spaces of sequences satisfying a certain axiom motivated by work of Hale and Kato for continuous time. We also give examples of these spaces. We consider the general cases when the linear part has a tempered exponential dichotomy and when the perturbation depends on a parameter. Moreover, we obtain the optimal regularity of the stable manifolds for Lipschitz and perturbations, jointly with respect to the base and to the parameter.

中文翻译：

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具有无限延迟的差分方程的稳定流形

我们为一大类具有无限延迟的非自治延迟差分方程构造稳定不变流形。这需要考虑一类合适的相空间，即满足由 Hale 和 Kato 工作连续时间激发的某个公理的序列的 Banach 空间。我们还给出了这些空间的例子。我们考虑线性部分具有缓和指数二分法以及扰动取决于参数时的一般情况。此外，我们获得了 Lipschitz 和扰动的稳定流形的最佳正则性，共同相对于基和参数。