(\phi f)(x) := \left \{ \begin{array}{cl}
\operatorname{sin} \frac{1}{x} & ,\quad x\in \langle 2k, 2k+1 ] , \; k\in \mathbb{Z} \\
f(x) & ,\quad x\in \langle 2k+1, 2k+2 ] , \; k\in \mathbb{Z} \\
 \end{array}