Zobrazeno 1 - 10
of 423
pro vyhledávání: '"Gomilko, A."'
Using a recently developed $\mathcal H$-calculus we propose a unified approach to the study of rational approximations of holomorphic semigroups on Banach spaces. We provide unified and simple proofs to a number of basic results on semigroup approxim
Externí odkaz:
http://arxiv.org/abs/2403.15894
Autor:
Gomilko, Alexander, Tomilov, Yuri
We improve the classical results by Brenner and Thom\'ee on rational approximations of operator semigroups. In the setting of Hilbert spaces, we introduce a finer regularity scale for initial data, provide sharper stability estimates, and obtain opti
Externí odkaz:
http://arxiv.org/abs/2403.14411
This paper investigates when analytic Besov functions of $n$ variables act on the generators of $n$ commuting $C_0$-semigroups on a Banach space. The theory for $n=1$ has already been published, and the present paper uses a different approach to that
Externí odkaz:
http://arxiv.org/abs/2311.18757
Autor:
Gomilko, Alexander, Tomilov, Yuri
We identify measures arising in the representations of products of generalized Stieltjes transforms as generalized Stieltjes transforms, provide optimal estimates for the size of those measures, and address a similar issue for generalized Cauchy tran
Externí odkaz:
http://arxiv.org/abs/2210.03474
This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups, in particu
Externí odkaz:
http://arxiv.org/abs/2202.03143
Autor:
Gomilko, Alexander, Tomilov, Yuri
Publikováno v:
In Journal of Functional Analysis 1 July 2024 287(1)
We construct two bounded functional calculi for sectorial operators on Banach spaces, which enhance the functional calculus for analytic Besov functions, by extending the class of functions, generalizing and sharpening estimates, and adapting the cal
Externí odkaz:
http://arxiv.org/abs/2101.05083
It is shown that in a class of counterexamples to Elliott's conjecture by Matomaki, Radziwill and Tao, the Chowla conjecture holds along a subsequence.
Externí odkaz:
http://arxiv.org/abs/2006.09958
We extend and deepen the theory of functional calculus for semigroup generators, based on the algebra $\mathcal B$ of analytic Besov functions, which we initiated in a previous paper. In particular, we show that our construction of the calculus is op
Externí odkaz:
http://arxiv.org/abs/1910.06369
It is proved that whenever a zero entropy dynamical system $(X,T)$ has only countably many ergodic measures and $\mu$ stands for the arithmetic M{\"o}bius function, then there exists a subset $A$ of integers depending only on the system, of logarithm
Externí odkaz:
http://arxiv.org/abs/1905.06563