Geodesic
On matrices with summable diagonals
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Tome 194 (2021), pp. 23-37.

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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.
Keywords: matrix with summable diagonals, method of similar operators, spectrum. 
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A. G. Baskakov; G. V. Garkavenko; N. B. Uskova. On matrices with summable diagonals. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Tome 194 (2021), pp. 23-37. http://geodesic.mathdoc.fr/item/INTO_2021_194_a2/

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