Maximally monotone operators are fundamental objects in modern optimization. The main classes of monotone operators are subdifferential operators and matrices with a positive semidefinite symmetric part. In this paper, we study a nice class of monotone operators: displacement mappings of isometries of finite order. We derive explicit formulas for resolvents, Yosida approximations, and (set-valued and Moore-Penrose) inverses. We illustrate our results by considering certain rational rotators and circular shift operators.

中文翻译：

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Isometries位移映射的分辨率和Yosida逼近

最大程度地，单调运算符是现代优化中的基本对象。单调算子的主要类别是亚微分算子和具有正半确定对称部分的矩阵。在本文中，我们研究了一类不错的单调算子：有限阶等距的位移映射。我们导出了明确的公式，用于解析子，Yosida近似和（集值和Moore-Penrose）逆。我们通过考虑某些有理旋转器和圆移位算子来说明我们的结果。