If φ is an analytic function mapping the unit disk D into itself, the composition operator Cφ is the operator on H 2 given by Cφf = f ◦φ. The structure of the composition operator Cφ is usually complex, even if the function φ is fairly simple. In this paper, we consider composition operators whose symbol φ is a linear fractional transformation mapping the disk into itself. That is, we will assu...

Let A(D) denote the disk algebra and uCφ be the weighted composition operator on A(D). In this paper, we characterize the compactness of sum of weighted composition operators on A(D). Furthermore, we also find the norm of sum of weighted composition operators on A(D). Mathematics Subject Classification: 47B33

We introduce the notion of diierential logic programs and we deene an operator for composing them in a hierarchical fashion. The semantics of this composition operator is reminiscent the semantics of inheritance of the object oriented paradigm. Similarly to classes in that paradigm, diierential programs can be organized in isa schemas where each component inherits or redeenes, modifying them, t...

In the previous work by Jacobs, Sokolova and the author, synchronous parallel composition of coalgebras—yielding a coalgebra—and parallel composition of behaviors—yielding a behavior, where behaviors are identified with states of the final coalgebra—were observed to form an instance of the microcosm principle. The microcosm principle, a term by Baez and Dolan, refers to the general phenomenon o...

We provide decomposition and quotienting results for multimodal logic with respect to a composition operator, traditionally used for epistemic models, due to van Eijck et al. (Journal of Applied NonClassical Logics 21(3–4):397–425, 2011), that involves sets of atomic propositions and valuation functions from Kripke models. While the composition operator was originally defined only for epistemic...