What is the effect on the cross-correlation of two windowed signals?

I've been trying to determine the effect of performing the cross-correlation operator on two windows signals.

For example: suppose we have two Sinc functions. The Sinc function is defined as $$\frac{sin(x)}{x}$$. The cross-correlation of these two signals is

\begin{align} R(\tau) &= \int_{-\infty}^{\infty} \overline{\textrm{sinc}(\pi t)} \cdot \textrm{sinc}(\pi\left(t + \tau\right))\space dt \\ &= \textrm{sinc}(\pi t) \end{align}

However, what would happen if this Sinc function is windowed by a windowing function $$w(t)$$ of length $$L$$? For the simplest case, what would happen if $$w(t)$$ is a boxcar function?

I've thought about this myself, and here is my reasoning: since the cross-correlation between two boxcar functions is equal to a triangular function, I was thinking this might be equal to: $$\textrm{sinc}(\pi t) \cdot \textrm{tri}(t)$$. Where the triangular function is non-zero between $$[-L, L]$$.

However, I am not able to proof that this is indeed the correct solution, and when I try this in the discrete domain, in code, I get a Sinc function that deviates from this solution.