Relevant Sampling of Band-limited Functions
  We study the random sampling of band-limited functions of several variables. If a bandlimited function with bandwidth one has its essential support on a cube of volume $R^d$, then $\cO (R^d \log R^d)$ random samples suffice to approximate the function up to a given error with high probability. 
Richard F. Bass and Karlheinz Gr\"ochenig
math.PR cs.IT math.IT