Is there any intuition for $\mathbb 1(-\Delta\leq \mu)$, where $\mu>0$, on $L^2(\mathbb R^d,\mathbb C^d)$, defined to be the "spectral projection of the Laplacian associated with the interval $(-\infty,\mu)$".
I understand the definition on the Fourier side: $\mathcal F [{\mathbb 1(-\Delta\leq \mu)\varphi}](\xi)=\mathbb 1(|\xi|^2\leq \mu)\widehat \varphi(\xi)$ for all $\varphi\in L^2(\mathbb R^d)$.
But what does this mean on the physical side? How does ${\mathbb 1(-\Delta\leq \mu)\varphi}$ compare to $\varphi$? It cuts off the high frequencies, so does it smooth out the function? I am struggling to understand.