Some Applied Aspects of Zygmund Function Classes

Working with signals we take into account their belonging to a certain class of signals. This belonging is given by the certain characteristic or set of characteristics peculiar for signals of this class. For most systems analysis problems related to signal theory, the question of their mathematical modeling arises. In such problems, the studied signal must be described by the certain function. Some characteristics of the signal correspond to certain properties of the function that this signal describes. This allows us to study the required signal characteristics as properties of a class of functions. Among the various classes of functions of systems analysis, Zygmund functions classes are the most popular from the practical point of view. When studying signals, we can describe them in the form of solutions of differential equations. This method of representation is very important in practice, as it helps to study the valuable signals properties from the practical point of view and helps to build certain approximations of the function that these signals model. In this paper, we have investigated the possibilities of approximation of the function from Zygmund class describing the signal by means of solutions of some second order differential equations in partial derivatives. The degree of signals approximation by solutions of biharmonic equations under certain boundary conditions has been obtained. A comparative analysis of the obtained degree of approximation at different values of the parameters characterizing Zygmund class has been made.