26 citations · 117 across the 42 of their papers we have counts for
42 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…
On regularity of compressions and diagonals of operator functions
Vladimir Müller, Yuri Tomilov
Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The settin…
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…
On growth and instability for semilinear evolution equations: an abstract approach
Vladimir Müller, Roland Schnaubelt, Yuri Tomilov
We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact no…