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of 460
pro vyhledávání: '"Michael Gil"'
Autor:
Michael Gil'
Publikováno v:
Opuscula Mathematica, Vol 44, Iss 2, Pp 241-248 (2024)
Let \(A\) be a bounded linear operator in a complex separable Hilbert space, \(A^*\) be its adjoint one and \(A_I:=(A-A^*)/(2i)\). Assuming that \(A_I\) is a Hilbert-Schmidt operator, we investigate perturbations of the imaginary parts of the eigenva
Externí odkaz:
https://doaj.org/article/8ea8c25405e34530ac73566e3babd159
Autor:
Michael Gil’
Publikováno v:
Bulletin of Mathematical Sciences, Vol 14, Iss 01 (2024)
Let [Formula: see text] and [Formula: see text] be bounded operators in a Banach space. For the equation [Formula: see text] we derive sharp explicit delay-dependent exponential stability conditions via the commutator [Formula: see text]. The stabili
Externí odkaz:
https://doaj.org/article/0abcfb71b19e44118aaa244f78b96d6c
Autor:
Michael Gil'
Publikováno v:
Opuscula Mathematica, Vol 41, Iss 3, Pp 395-412 (2021)
Let \(A\) and \(\tilde{A}\) be bounded operators in a Hilbert space. We consider the following problem: let the spectrum of \(A\) lie in some strip. In what strip the spectrum of \(\tilde{A}\) lies if \(A\) and \(\tilde{A}\) are "close"? Applications
Externí odkaz:
https://doaj.org/article/5340146c9ad94b6badf6cf2f75c08448
Autor:
Michael Gil'
Publikováno v:
Communications in Advanced Mathematical Sciences, Vol 2, Iss 2, Pp 129-134 (2019)
Let $A$ and $B$ be linear operators on a Hilbert space. Let $A$ and $A+B$ generate $C_0$-semigroups $e^{tA}$ and $e^{t(A+B)}$, respectively, and $e^{tA}$ be exponentially stable. We establish exponential stability conditions for $e^{t(A+B)}$ in terms
Externí odkaz:
https://doaj.org/article/c0e7126a6248468ea3b40cacbcee2336
Autor:
Michael Gil'
Publikováno v:
Universal Journal of Mathematics and Applications, Vol 2, Iss 2, Pp 94-99 (2019)
We suggest a bound for the joint spectral radius of a finite set of operators in a Hilbert space. In appropriate situations that bound enables us to avoid complicated calculations and gives a new explicit stability test for the discrete time switched
Externí odkaz:
https://doaj.org/article/f97a094e2e8f46bf88fab96e9732fb20
Autor:
Michael Gil’
Publikováno v:
Axioms, Vol 10, Iss 2, p 99 (2021)
The paper is a survey of the recent results of the author on the perturbations of matrices. A part of the results presented in the paper is new. In particular, we suggest a bound for the difference of the determinants of two matrices which refines th
Externí odkaz:
https://doaj.org/article/3e7de2b6e6a14e95abdc3df30f743844
Autor:
Michael Gil'
Publikováno v:
Opuscula Mathematica, Vol 35, Iss 2, Pp 161-169 (2015)
The paper deals with operators of the form \(A=S+B\), where \(B\) is a compact operator in a Hilbert space \(H\) and \(S\) is an unbounded normal one in \(H\), having a compact resolvent. We consider approximations of the eigenvectors of \(A\), corre
Externí odkaz:
https://doaj.org/article/023fb32a2a464464a97ca619efd319ef
Autor:
Michael Gil’
Publikováno v:
Axioms, Vol 8, Iss 1, p 20 (2019)
The paper is devoted to the discrete Lyapunov equation X − A * X A = C , where A and C are given operators in a Hilbert space H and X should be found. We derive norm estimates for solutions of that equation in the case of unstable operator A, as we
Externí odkaz:
https://doaj.org/article/466e979493b545d5b3b06d2d42e2aec1
Autor:
Michael Gil'
Publikováno v:
Electronic Journal of Differential Equations, Vol 2013, Iss 137,, Pp 1-7 (2013)
We consider a linear homogeneous functional differential equation with delay in a Banach space. It is proved that if the corresponding non-homogeneous equation, with an arbitrary free term bounded on the positive half-line and with the zero initial c
Externí odkaz:
https://doaj.org/article/3fb82abec6234352802e89b4d832a01c
Autor:
Michael Gil'
Publikováno v:
Opuscula Mathematica, Vol 33, Iss 2, Pp 283-291 (2013)
Let \(\{p_k\}\) be a nondecreasing sequence of integers, and \(A\) be a compact operator in a Hilbert space whose eigenvalues and singular values are \(\lambda_k(A)\) and \(s_k(A)\) \((k=1, 2, .... )\), respectively. We establish upper and lower boun
Externí odkaz:
https://doaj.org/article/2d325ad493364712b16a9d7ed9516c07