V. Kurbatov

activity

20152021

collaborators

8 papers

math.NA2021

An estimate of approximation of an analytic function of a matrix by a rational function

M. Ferus, V. G. Kurbatov, I. V. Kurbatova

Let $A$ be a square complex matrix; $z_{1}$ , ..., $z_{N} \in C$ be arbitrary (possibly repetitive) points of interpolation; $f$ be an analytic function defined on a neighborhoo…

math.NA2021

Calculating a function of a matrix with a real spectrum

P. Kubelík, V. G. Kurbatov, I. V. Kurbatova

Let $T$ be a square matrix with a real spectrum, and let $f$ be an analytic function. The problem of the approximate calculation of $f (T)$ is discussed. Applying the Schur triangul…

math.FA2020

Inverse-closedness of the subalgebra of locally nuclear operators

E. Yu. Guseva, V. G. Kurbatov

Let $X$ be a Banach space and $T$ be a bounded linear operator acting in $l_{p} (Z^{c}, X)$ , $1 \leq p \leq \infty$ . The operator $T$ is called \emph{locally nuclear} if it can be rep…

math.FA2018

Inverse-closedness of subalgebras of integral operators with almost periodic kernels

E. Yu. Guseva, V. G. Kurbatov

The integral operator of the form $(N u) (x) = k = 1 \sum \infty e^{i ⟨ ω_{k}, x ⟩} \int_{R^{c}} n_{k} (x - y) u (y) d y$ acting in $L_{p} (R^{c})$ , $1\le p\le\inf…

math.FA2018

Green's function of the problem of bounded solutions in the case of a block triangular coefficient

V. G. Kurbatov, I. V. Kurbatova

It is known that the equation $x^{'} (t) = A x (t) + f (t)$ , where $A$ is a bounded linear operator, has a unique bounded solution $x$ for any bounded continuous free term~ $f$ if and only if…

math.FA2017

The Gelfand--Shilov type estimate for Green's function of the bounded solutions problem

V. G. Kurbatov, I. V. Kurbatova

An analog of the Gelfand--Shilov estimate of the matrix exponential is proved for Green's function of the problem of bounded solutions of the ordinary differential equation $x'(t)-…