On Representation of a Class of Continuous Functions by a Discrete Set of Their Values

We prove a theorem which allows us to represent each continuous function from a certain class by a discrete set of its values that correspond to equidistant values of the argument. For a particular case where the continuous functions are fundamental oscillations of dynamical systems with lumped parameters, we suggest a simple method for graphically determining the argument quantization step sufficient for representation of these functions by a discrete set of their values.