Standard

On Location of the Matrix Spectrum with Respect to a Parabola. / Demidenko, G. V.; Prokhorov, V. S.

In: Siberian Advances in Mathematics, Vol. 33, No. 3, 08.2023, p. 190-199.

Research output: Contribution to journal › Article › peer-review

Harvard

Demidenko, GV & Prokhorov, VS 2023, 'On Location of the Matrix Spectrum with Respect to a Parabola', Siberian Advances in Mathematics, vol. 33, no. 3, pp. 190-199. https://doi.org/10.1134/S1055134423030033

APA

Demidenko, G. V., & Prokhorov, V. S. (2023). On Location of the Matrix Spectrum with Respect to a Parabola. Siberian Advances in Mathematics, 33(3), 190-199. https://doi.org/10.1134/S1055134423030033

Vancouver

Demidenko GV, Prokhorov VS. On Location of the Matrix Spectrum with Respect to a Parabola. Siberian Advances in Mathematics. 2023 Aug;33(3):190-199. doi: 10.1134/S1055134423030033

Author

Demidenko, G. V. ; Prokhorov, V. S. / On Location of the Matrix Spectrum with Respect to a Parabola. In: Siberian Advances in Mathematics. 2023 ; Vol. 33, No. 3. pp. 190-199.

BibTeX

@article{07a0982185034841a51a481176e2f7e4,
title = "On Location of the Matrix Spectrum with Respect to a Parabola",
abstract = "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.",
keywords = "Krein{\textquoteright}s theorem, generalized Lyapunov equations, location of the matrix spectrum, theorem on dichotomy",
author = "Demidenko, {G. V.} and Prokhorov, {V. S.}",
note = "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.",
year = "2023",
month = aug,
doi = "10.1134/S1055134423030033",
language = "English",
volume = "33",
pages = "190--199",
journal = "Siberian Advances in Mathematics",
issn = "1055-1344",
publisher = "PLEIADES PUBLISHING INC",
number = "3",

}

RIS

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 -

ID: 59563927