27 research outputs found
Generation of subordinated holomorphic semigroups via Yosida's theorem
Using functional calculi theory, we obtain several estimates for
, where is a Bernstein function, is a bounded
completely monotone function and is the generator of a holomorphic
-semigroup on a Banach space, bounded on . Such estimates are
of value, in particular, in approximation theory of operator semigroups. As a
corollary, we obtain a new proof of the fact that generates a
holomorphic semigroup whenever does, established recently in [8] by a
different approach
Product formulas in functional calculi for sectorial operators
We study the product formula in the framework of
(unbounded) functional calculus of sectorial operators . We give an abstract
result, and, as corollaries, we obtain new product formulas for the holomorphic
functional calculus, an extended Stieltjes functional calculus and an extended
Hille-Phillips functional calculus. Our results generalise previous work of
Hirsch, Martinez and Sanz, and Schilling.Comment: This is the authors accepted manuscript for a paper being published
in Mathematische Zeitschrift. The final publication is available at Springer
via http://dx.doi.org/10.1007/s00209-014-1378-
Sarnak's conjecture implies the Chowla conjecture along a subsequence
We show that the M\"obius disjointess of zero entropy dynamical systems
implies the existence of an increasing sequence of positive integers along
which the Chowla conjecture on autocorrelations of the M\"obius function holds.Comment: Proceedings of the Chair Morlet semester "Ergodic Theory and
Dynamical Systems in their Interactions with Arithmetic and Combinatorics"
1.08.2016--31.01.2017, Springer, to appea
Resolvent representations for functions of sectorial operators
We obtain integral representations for the resolvent of , where
is a holomorphic function mapping the right half-plane and the right
half-axis into themselves, and is a sectorial operator on a Banach space.
As a corollary, for a wide class of functions , we show that the operator
generates a sectorially bounded holomorphic -semigroup on a
Banach space whenever does, and the sectorial angle of is preserved.
When is a Bernstein function, this was recently proved by Gomilko and
Tomilov, but the proof here is more direct. Moreover, we prove that such a
permanence property for can be described, at least on Hilbert spaces, in
terms of the existence of a bounded -calculus for . As
byproducts of our approach, we also obtain new results on functions mapping
generators of bounded semigroups into generators of holomorphic semigroups and
on subordination for Ritt operators.Comment: The paper has been accepted for publication in Advances in
Mathematics. This is the authors' accepted versio
A Besov algebra calculus for generators of operator semigroups and related norm-estimates
We construct a new bounded functional calculus for the generators of bounded
semigroups on Hilbert spaces and generators of bounded holomorphic semigroups
on Banach spaces. The calculus is a natural (and strict) extension of the
classical Hille-Phillips functional calculus, and it is compatible with the
other well-known functional calculi. It satisfies the standard properties of
functional calculi, provides a unified and direct approach to a number of
norm-estimates in the literature, and allows improvements of some of them.Comment: This is the authors' accepted version of a paper which will be
published in Mathematische Annale