V. Kurbatov

activity

20152023

most citedAnalytic functional calculus for two operators

5 citations · 7 across the 10 of their papers we have counts for

collaborators

11 papers

math.NA2023

An approximation of matrix exponential by a truncated Laguerre series

E. D. Khoroshikh, V. G. Kurbatov

The Laguerre functions $l_{n, τ}^{α}$ , $n = 0, 1, \dots$ , are constructed from generalized Laguerre polynomials. The functions $l_{n, τ}^{α}$ depend on two parameters: scale $τ > 0$ and order…

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.NA2018

An estimate of approximation of a matrix-valued function by an interpolation polynomial

V. G. Kurbatov, I. V. Kurbatova

Let $A$ be a square complex matrix, $z_{1}$ , ..., $z_{n} \in C$ be (possibly repetitive) points of interpolation, $f$ be analytic in a neighborhood of the convex hull of the un…

math.FA2018★ 1 cited

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)-…

math.NA2017★ 1 cited

Computation of Green's function of the bounded solutions problem

V. G. Kurbatov, I. V. Kurbatova

It is well known that the equation $x^{'} (t) = A x (t) + f (t)$ , where $A$ is a square matrix, has a unique bounded solution $x$ for any bounded continuous free term $f$ , provided the coeffi…

math.FA2016★ 5 cited

Analytic functional calculus for two operators

V. G. Kurbatov, I. V. Kurbatova, M. N. Oreshina

Properties of the mappings \begin{align*} C&\mapsto\frac1{(2πi)^2}\int_{Γ_1}\int_{Γ_2}f(λ,μ)\,R_{1,\,λ}\,C\, R_{2,\,μ}\,dμ\,dλ, C&\mapsto\frac1{2πi}\int_Γg(λ)R_{1,\,λ}\,C\, R_{2,\,…

math.FA2015

Inverse-closedness of the set of integral operators with $L_{1}$ -continuously varying kernels

V. G. Kurbatov, V. I. Kuznetsova

Let $N$ be an integral operator of the form $(N u) (x) = \int_{R^{c}} n (x, x - y) u (y) d y$ acting in $L_{p} (R^{c})$ with a measurable kernel $n$ satisfying the estima…

An approximation of matrix exponential by a truncated Laguerre series

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

Calculating a function of a matrix with a real spectrum

Inverse-closedness of the subalgebra of locally nuclear operators

An estimate of approximation of a matrix-valued function by an interpolation polynomial

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

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

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

Computation of Green's function of the bounded solutions problem

Analytic functional calculus for two operators

Inverse-closedness of the set of integral operators with L1​-continuously varying kernels

Inverse-closedness of the set of integral operators with $L_{1}$ -continuously varying kernels