Applied Aspects of Polyharmonic Functions for Security and Reliability of Data Transmission

At present, when armed conflicts have intensified, and especially against the background of Russia's armed aggression against Ukraine, a new era of development of high-precision means of protection and weapons has begun. Their effectiveness is primarily determined by the state of radio-electronic technical means. These include means of communication and control, radar and hydroacoustics, telemetry, etc. Thus, the effectiveness of the solution of the tasks before the radio-electronic device depends on the class of signals used. In particular, the type of signal depends on the quality of the communication, the range, the resolution capabilities according to various parameters, the probability of detection, the quality of control, stealth, etc. But the detection of hidden signals requires high-quality signal processing with consistent mathematical analysis of the signal. This requires a powerful mathematical apparatus. As an example of signal processing, the article discusses methods of using signal transformation using polyharmonic operators. The transformation of signals by two types of operators is presented: the Abel-Poisson operator and the Weierstrass operator. The simulation results proved the advantages of Weierstrass operators for signal transformation.