V. Kurbatov

activity

20152023

collaborators

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6 papers · 1 filter

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)-…

math.FA2016

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…