TY - JOUR

T1 - On Location of the Matrix Spectrum with Respect to a Parabola

AU - Demidenko, G. V.

AU - Prokhorov, V. S.

N1 - The study was carried out within the framework of the state contract for the Sobolev Institute of Mathematics of the Siberian Branch of RAS (project No. FWNF-2022-0008). Публикация для корректировки.

PY - 2023/8

Y1 - 2023/8

N2 - In the present article, we consider the problem on location of the matrix spectrum withrespect to a parabola. In terms of solvability of a matrix Lyapunov type equation, we provetheorems on location of the matrix spectrum in certain domains (Formula presented.) (bounded by a parabola) and (Formula presented.) (lying outside the closure of (Formula presented.)). A solution to the matrix equation is constructed.We use this equation and prove an analog of the Lyapunov–Krein theorem on dichotomy ofthe matrix spectrum with respect to a parabola.

AB - In the present article, we consider the problem on location of the matrix spectrum withrespect to a parabola. In terms of solvability of a matrix Lyapunov type equation, we provetheorems on location of the matrix spectrum in certain domains (Formula presented.) (bounded by a parabola) and (Formula presented.) (lying outside the closure of (Formula presented.)). A solution to the matrix equation is constructed.We use this equation and prove an analog of the Lyapunov–Krein theorem on dichotomy ofthe matrix spectrum with respect to a parabola.

KW - Krein’s theorem

KW - generalized Lyapunov equations

KW - location of the matrix spectrum

KW - theorem on dichotomy

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85169662264&origin=inward&txGid=461448506aa26f3f96a620586a95a455

UR - https://www.mendeley.com/catalogue/018ba1b4-fa64-3c8c-b76a-8feab459566f/

U2 - 10.1134/S1055134423030033

DO - 10.1134/S1055134423030033

M3 - Article

VL - 33

SP - 190

EP - 199

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 3

ER -