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The report consists from the following two parts. In the first part, application of the constructive approximation theory on the base of the atomic functions to problems of antenna analysis and synthesis. New methods of signal approximation with the help of compactly supported atomic functions and the Whittaker–Kotel’nikov–Shannon theorem are considered and justified. The second part of the report is devoted to the Boolean algebra transformations and R-functions theory. An algorithm for description of arbitrary star-shaped domains boundaries in polar coordinates is proposed. Using these equations, a new schemes for amplitude-phase synthesis of complex-shaped flat and curvilinear antennas are proposed.

atomic function; R-function