I have a multivariable function that is composed of six variables; four of these are constants $C}_{1},{C}_{2},{C}_{3},{C}_{4$ and the other two variables are x and y. The function is defined as follows

$Xi(x,y,{C}_{1},{C}_{2},{C}_{3},{C}_{4})$ I would like to find the maximum value of $Xi$ over $x\in \{-\mathrm{\infty},\mathrm{\infty}\}$ and $y\in \{-\mathrm{\infty},\mathrm{\infty}\}$ . What is the rigorous mathematical notation I should use to describe this. Is this fine:

$max\left\{Xi(x,y,{C}_{1},{C}_{2},{C}_{3},{C}_{4})\right\}$