FUNCTIONS THAT ARE UNIVERSAL WITH RESPECT TO THE CLASSICAL SYSTEMS

Further, characteristics and structures of universal functions will be revealed. Problems with the existence and structure of universal pairs for classica systems will be studied and solved.

Numerous works of famous mathematicians are devoted to the existence of functions, which are universal in different senses.

In the above-mentioned results the universality of the functions was manifested by the sequence of ‘additive translates’ , by the differencet quotients,, by the high order derivatives and by theTaylor series respectively.

We will construct functions such that their universality is manifested through their Fourier coefficients with respect to the classical systems.

The research team is planning to solve the problems conserning the existence, properties as well as the structure of universal functions in different senses with respect to the classical (trigonometric, Walsh, Haar, Shauder, Franklin, Wilenkin) systems for the following functional classes: ; and . Problems concerning to the existence and structure of universal pairs with respect to the classical systems will be studied and solved.