I understand that the Nyquist sampling theorem dictates that the minimum sampling frequency, $f_s$, be s.t. $f_s > 2B$, where $ B $, is the bandwidth of the signal. I have read the explanation for what happens when the input signal contains an impulse/non zero ferquency spectrum at $fs = fm$. But is there any way to do a mathematical proof that sampling at $fs = 2B$ works when the signal is strictly bandlimited.
A little background : This is a HW problem
The given hint was to use the fact that "one way to interpret Nyquist Sampling theorem is to note that any bandlimited signal can be represented as a superposition of bandlimited signals that are orthogonal to each other."