Displaying similar documents to “Cosine operator functions”

Isolated points of some sets of bounded cosine families, bounded semigroups, and bounded groups on a Banach space

Adam Bobrowski, Wojciech Chojnacki (2013)

Studia Mathematica

Similarity:

We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space 𝓛(X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family whose members are all scalar multiples of the identity operator. We also show that if the sets...

Hille-Yosida type theorems for local regularized semigroups and local integrated semigroups

Sheng Wang Wang (2002)

Studia Mathematica

Similarity:

Motivated by a great deal of interest recently in operators that may not be densely defined, we deal with regularized semigroups and integrated semigroups that are either not exponentially bounded or not defined on [0,∞) and generated by closed operators which may not be densely defined. Some characterizations and related examples are presented. Our results are extensions of the corresponding results produced by other authors.

Almost-distribution cosine functions and integrated cosine functions

Pedro J. Miana (2005)

Studia Mathematica

Similarity:

We introduce the notion of almost-distribution cosine functions in a setting similar to that of distribution semigroups defined by Lions. We prove general results on equivalence between almost-distribution cosine functions and α-times integrated cosine functions.

Perturbations of bi-continuous semigroups

Bálint Farkas (2004)

Studia Mathematica

Similarity:

The notion of bi-continuous semigroups has recently been introduced to handle semigroups on Banach spaces that are only strongly continuous for a topology coarser than the norm-topology. In this paper, as a continuation of the systematic treatment of such semigroups started in [20-22], we provide a bounded perturbation theorem, which turns out to be quite general in view of various examples.

Frequently hypercyclic semigroups

Elisabetta M. Mangino, Alfredo Peris (2011)

Studia Mathematica

Similarity:

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 integral. This criterion can be verified in certain cases in terms of the infinitesimal generator of the semigroup. Applications are given for semigroups generated by Ornstein-Uhlenbeck operators, and especially for translation semigroups on weighted...