I have one vector $V_{2}$ that never changes. I have another vector $V_{1}$ that changes based on some small shift in t. Should I write this as $V_{1}(t+\Delta t)$? These vectors are discrete sets with n elements, and it is not possible (for my application) to turn these vectors into continuous functions. As written, it looks like it is a function, but in reality it is really just m number of V1's for m number of t shifts.
Finally, I take the dot product between all the $V_{1}$ vectors (that result from all inputs in a range of $\pm \Delta t$) and $V_{2}$, and subtract the $\Delta t$ I used to get the respective $V_{1}$. This results in a new vector of dot products on length m elements. How would I mathematically express finding the maximum of this set? Do I need specific notation to denote these vectors as vectors?