On matrices with summable diagonals

In this paper, basic concepts and facts related to infinite matrices are considered. The matrix (operator) approach is applied to the proof of Wiener's theorem on absolutely convergent Fourier series. A modification of the method of similar operators related to the Friedrichs equation is studied. Using the method of similar operators, we reduce a strictly lower triangular matrix with summable diagonals to the diagonal (block diagonal) form; this allows one to find the spectrum.