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

Resolvents and Yosida Approximations of Displacement Mappings of Isometries