Resolvents and Yosida approximations of displacement mappings of isometries

Abstract

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 MoorePenrose) inverses. We illustrate our results by considering certain rational rotators and circular shift operators.