26 citations · 53 across the 24 of their papers we have counts for
25 papers
Beurling--Kato theory, Hardy--Sobolev calculus and Ritt operators
A. Borichev, A. Gomilko, Yu. Tomilov
We develop a discrete Beurling--Kato theory for bounded operators and relate it to a Hardy--Sobolev functional calculus on Stolz domains. Our central class is that of Ritt operator…
Asymptotic behavior of solutions to the Dirac system with respect to a spectral parameter
Alexander Gomilko, Łukasz Rzepnicki
We consider the Dirac system of ordinary differential equations \[ Y'(x) + \begin{bmatrix} 0 & σ_1(x) \\ σ_2(x) & 0 \end{bmatrix} Y(x) = iμ\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmat…
Rational approximation of operator semigroups via the -calculus
Alexander Gomilko, Yuri Tomilov
We improve the classical results by Brenner and Thomée on rational approximations of operator semigroups. In the setting of Hilbert spaces, we introduce a finer regularity scale fo…
Rational approximation of holomorphic semigroups revisited
Charles Batty, Alexander Gomilko, Yuri Tomilov
Using a recently developed -calculus we propose a unified approach to the study of rational approximations of holomorphic semigroups on Banach spaces. We provide unifie…
Analytic Besov functional calculus for several commuting operators
Charles Batty, Alexander Gomilko, Dominik Kobos +1
This paper investigates when analytic Besov functions of variables act on the generators of commuting -semigroups on a Banach space. The theory for has already b…
To the theory of generalized Stieltjes transforms
Alexander Gomilko, Yuri Tomilov
We identify measures arising in the representations of products of generalized Stieltjes transforms as generalized Stieltjes transforms, provide optimal estimates for the size of t…