Method of similar operators in the study of spectral properties of perturbed first-order differential operators

A. G. Baskakov ; I. A. Krishtal ; N. B. Uskova

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 3-18.

Résumé

In this paper, we considers first-order differential operators with periodic boundary conditions acting in a Hilbert space of square summable functions on the segment $[0,\omega] $ perturbed by Hilbert–Schmidt integral operators. A similarity transformation of the original operator to the operator of the block-diagonal structure is performed; this allows one to study spectral properties of the perturbed operator. The research method is the method of similar operators, which also presented in this work.

Détail

Keywords: method of similar operators, spectrum, integro-differential operator.

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