System analysis and grounding for the data processing means and technologies based on ateb-functions

There is given the grounding of possibility to use Ateb-functions for solving special communication problems in terms of the convolution *-algebras formalism in which the multiplication is defined by means of hypergroups of generalized shift operators introduced to mathematics by J. Delsarte in 1956 17. As it has been shown in 1972 (see 3), defined by such hypergroup convolution carries on obvious way to Parseval's theorem and accomplishment by time component for the systems and signals analysis. Application of this fact to the case of Ateb-basis signifies the complishment of mathematical instrumentation of analysis on the base of Ateb-functions. The exposition is argumented by historical facts and quotations concerning to the problem in question. This material confirms the necessity for applying of renewed system analysis in each case to take into account changed situation under grounding the mathematical model used in the problem to be solved and choice of an adequate method for this.