We construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, Sér. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser (1992), and a similar decomposition when M is the sphere by Bownik and Dziedziul (Const. Approx., 41, 23–48 2015).

中文翻译：

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黎曼流形上的平滑正交投影

我们构造黎曼流形M上恒等式算子的分解，该分解为服从M的开放覆盖的平滑正交投影的总和。由于Coifman和Meyer（CR Acad。Sci。Paris，Sér。I Math。，312（3），259-261 1991）和Auscher，Weiss，Wickerhauser（1992），这通过平滑的正交投影在实线上扩展了分解。，当类似的分解中号是由Bownik和Dziedziul（常数。约，球体41，23-48 2015）。