Checking the Regularity of the Linear Method of Summation Fourier Series

Systems analysis is a powerful tool for studying complex systems of various natures. Periodic signals can be represented by orthogonal systems of functions. Examples of such orthogonal systems are Walsh system, Chebyshev system and others. The system of trigonometric functions of sines and cosines of multiple arguments has become the most widespread. But, as we know, there are examples of continuous functions, the Fourier series of which diverge at some points. Series summation methods make it possible to match a divergent series to some ”sum”. An example of a matrix with convenient elements for checking the necessary and sufficient conditions for the regularity of the rectangular summation method is given.