Applications of atomic functions to the boundary value problems, signal processing, and synthesis of antennas

This paper presents and focused primarily on the application of atomic to signal processing, image reconstruction, which is also the subject of the recent publications. However, the potential capabilities of this mathematical tool are quite diverse and they can find wide application of elastic waves, etc. They can be used as the basis functions for solving problems of electrodynamics, antenna analysis and synthesis, etc. Moreover, they can be used in acousto and opto-electronics as well as in signal processing problems in medical equipment in combination with other approaches. For short, it is impossible to consider the capabilities of the theory of atomic functions.