We show that spectral data of the Koopman operator arising from an analytic expanding circle map can be effectively calculated using an EDMD-type algorithm combining a collocation method of order with a Galerkin method of order . The main result is that if , where is an explicitly given positive number quantifying by how much expands concentric annuli containing the unit circle, then the method converges and approximates the spectrum of the Koopman operator, taken to be acting on a space of analytic hyperfunctions, exponentially fast in . Additionally, these results extend to more general expansive maps on suitable annuli containing the unit circle.

中文翻译：

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用于扩展圆图及其复杂扰动的 EDMD


我们证明，使用结合阶数搭配方法和伽辽金阶数方法的 EDMD 型算法，可以有效地计算由解析扩展圆图产生的 Koopman 算子的谱数据。主要结果是，如果 ，其中 是一个明确给定的正数，量化包含单位圆的同心圆环的扩展程度，则该方法收敛并近似库普曼算子的谱，该算子作用于解析超函数的空间，呈指数级快速增长。此外，这些结果扩展到包含单位圆的合适环上的更一般的扩展图。