Related papers: On some properties of multidimensional Bochner-Phi…
The functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the condition for holomorphy of semigroups, generated by operators which arisen in the calculus is given, and in…
The paper deals with (multidimensional and one-dimensional) Bochner-Phillips functional calculus. Bounded perturbations of Bernstein functions of (one or several commuting) semigroup generators on Banach spaces are considered, conditions…
The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is considered. Connections of this calculus to Bochner-Phillips functional calculus are indicated. In particular, the…
The paper deals with multidimensional Bochner-Phillips functional calculus. In the previous paper by the author bounded perturbations of Bernstein functions of several commuting semigroup generators on Banach spaces where considered,…
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…
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…
The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is given. Connections of this calculus to Bochner-Phillips functional calculus are indicated, and several examples are…
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,…
Let $\psi$ be a Bernstein function in one variable. A.~Carasso and T.~Kato obtained necessary and sufficient conditions for $\psi$ to have a property that $\psi(A)$ generates a quasibounded holomorphic semigroup for every generator $A$ of a…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
In this article we apply a recently established transference principle in order to obtain the boundedness of certain functional calculi for semigroup generators. In particular, it is proved that if $-A$ generates a $C_0$-semigroup on a…
In this short note we use ideas from systems theory to define a functional calculus for infinitesimal generators of strongly continuous semigroups on a Hilbert space. Among others, we show how this leads to new proofs of (known) results in…
This paper examines the coefficient problems for the class of semigroup generators, a topic in complex dynamics that has recently been studied in context of geometric function theory. Further, sharp bounds of coefficient functional such as…
Using functional calculi theory, we obtain several estimates for $\|\psi(A)g(A)\|$, where $\psi$ is a Bernstein function, $g$ is a bounded completely monotone function and $-A$ is the generator of a holomorphic $C_0$-semigroup on a Banach…
In this paper we develop a functional calculus for a countable system of generators of contraction strongly continuous semigroups. As a symbol class of such calculus we use the algebra of polynomial tempered distributions. We prove a…
Model structures for many different kinds of functor calculus can be obtained by applying a theorem of Bousfield to a suitable category of functors. In this paper, we give a general criterion for when model categories obtained via this…
We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard's theorem for moment functionals is proven. The notion of semi-classical bilinear functionals is introduced as a generalization…
We present a functional calculus approach to the study of rates of decay in mean ergodic theorems for bounded strongly continuous operator semigroups. A central role is played by operators of the form $g(A)$, where $-A$ is the generator of…
We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis…
In the spectral theory of non-self-adjoint operators there is a well-known operation of product of operator colligations. Many similar operations appear in the theory of infinite-dimensional groups as multiplications of double cosets. We…