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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 , where is a bounded linear operator, has a unique bounded solution for any bounded continuous free term~ 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★ 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,\,…