5 papers
An estimate of approximation of an analytic function of a matrix by a rational function
M. Ferus, V. G. Kurbatov, I. V. Kurbatova
Let be a square complex matrix; , ..., be arbitrary (possibly repetitive) points of interpolation; be an analytic function defined on a neighborhoo…
Calculating a function of a matrix with a real spectrum
P. Kubelík, V. G. Kurbatov, I. V. Kurbatova
Let be a square matrix with a real spectrum, and let be an analytic function. The problem of the approximate calculation of is discussed. Applying the Schur triangul…
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…
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)-…
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,\,…