Estimates for Harmonic Operators in Modeling Application Processes
Valentyn Sobchuk, Serhiі Laptiev, Андрій Собчук, Iryna Zamrii, Volodymyr Nakonechnyi, Yurii Shcheblanin · 2022
The report investigates the mathematical apparatus of harmonic operators, which can be used for modeling the processing of the amplitude-frequency spectrum of dynamic objects. The proposed results can be used for field modeling of relevant real objects that allow for appropriate interpretation. It is shown that for a harmonic operator represented by a Poisson operator the deviation in the spectrum of signals from the main signal will not exceed $\beta\text{ln}\displaystyle \frac{1}{\beta}$.. For the case when the biharmonic Poisson integral is represented as a harmonic operator, the deviation in the spectrum of signals from the main signal will not exceed $\beta$. The results of the study allow the use of the apparatus of harmonic operators to model applied problems, which are reduced to problems based on the Fourier transform apparatus in the processing of streaming data