Let $ t$ be a real number such that present the time. Really am interesting to know if there exists an operator satisfies the below property:
$$A^{-1}(t)=A(-t+ i \beta)$$ $\beta$ is a real number non-null and $ A^{-1} $ is the compositional inverse of $ A$ , For instance I have got only the Unitary Operator as exponential form which it's used widely in quantum mechanics as shown here but it satisfies only :$U^{-1}(t)=U(-t)$
Note 01: In Have edited my question without changing the meaning of it and for the given answer , I didn't meant by U in my titled equality the unitary operator but it is an operator which i search on it
Note 02: The motivation of this question is to know more about chaotic operators