A deterministic view on the capacity of bandlimited functions

In this paper, the relationship between Kolmogorov´s capacity and Shannon´s capacity in the context of communication with square-intgrable, bandlimited signals subject to additive noise is illustrated. Upper and lower bounds on the Kolmogorov capacity are derived, that improve upon previous results. The functional form of these bounds is analogous to the one of the capacity of the additive white Gaussian noise channel, showing an essential similarity between the deterministic and the stochastic approaches, and suggesting that communication limits are a fundamental physical concept that transcends the details of the specific mathematical description chosen for their representation.