let $varphi(z)=z^m, z in mathbb{u}$, for some positive integer $m$, and $c_varphi$ be the composition operator on the bergman space $mathcal{a}^2$ induced by $varphi$. in this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $c^*_varphi c_varphi, c_varphi c^*_varphi$ as well as self-commutator and anti-self-commutators of $c_...

Model composition helps designers managing complexities by modeling different system views separately, and later compose them into an integrated model. In the past years, researchers have focused on the definition of model composition approaches (operators) and the tools supporting them (model composition engines). Testing model composition engines is hard. It requires the synthesis and analysi...

We introduce a new operator for general rationing problems in which, besides conflicting claims, individual baselines play an important role in the rationing process. The operator builds onto ideas of composition, which are not only frequent in rationing, but also in related problems such as bargaining, choice, and queuing. We characterize the operator and show how it preserves some standard ax...

Recommended by Shusen Ding Let D denote the open unit disk in the complex plane and let dAz denote the normalized area measure on D. Φ α is defined as follows L Φ α {f ∈ HD : D ΦΦlog |fz|1 − |z| 2 α dAz < ∞}. Let ϕ be an analytic self-map of D. The composition operator C ϕ induced by ϕ is defined by C ϕ f f • ϕ for f analytic in D. We prove that the composition operator C ϕ is compact on L Φ α ...

This paper is the first attempt to introduce the operator of composition, already known from probability, possibility and evidence theories, also for credal sets. We prove that the proposed definition preserves all the necessary properties of the operator enabling us to define compositional models as an efficient tool for multidimensional models representation. Theoretical results are accompani...

This paper treats a high-level, algebraic programming method for the on-line control of actions in a realtime, parallel processing environment. The method is based on interaction of path expressions. On the basis of a set of path expressions evocation of actions can be controlled in realtime in a fully automated way. It is shown how intelligent system behaviour can be obtained by a combination ...

A function theoretic characterization is given of when a composition operator is compact on BMOA, the space of analytic functions on the unit disk having radial limits that are of bounded mean oscillation on the unit circle. When the symbol of the composition operator is univalent, compactness on BMOA is shown to be equivalent to compactness on the Bloch space, and a characterization in terms o...