Composition operators Cφ on the Hilbert Hardy space H 2 over the unit disk are considered. We investigate when convergence of sequences {φn} of symbols, (i.e., of analytic selfmaps of the unit disk) towards a given symbol φ, implies the convergence of the induced composition operators, Cφn → Cφ . If the composition operators Cφn are Hilbert–Schmidt operators, we prove that convergence in the Hi...

We show that if a small holomorphic Sobolev space on the unit disk is not just small but very small, then a trivial necessary condition is also sufficient for a composition operator to be bounded. A similar result for holomorphic Lipschitz spaces is also obtained. These results may be viewed as boundedness analogues of Shapiro’s theorem concerning compact composition operators on small spaces. ...

The paper addresses the problem of solving equations over languages, that model the problem of synthesizing an unknown component, both in hardware and software systems. We investigate what algebraic properties must be satisfied by a composition operator so that the related language equation yields a general solution of the same form, and show sufficient conditions to derive such a largest solut...

Composition operators on the Hilbert Hardy space of the unit disk are considered. The shape of their numerical range is determined in the case when the symbol of the composition operator is a monomial or an inner function fixing 0. Several results on the numerical range of composition operators of arbitrary symbol are obtained. It is proved that 1 is an extreme boundary point if and only if 0 i...

We consider differences of weighted composition operators between given weighted Bergman spaces H∞ v of infinite order and characterize boundedness and the essential norm of these differences.

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.

We study when weighted composition operators Cφ,ψ acting between weighted Bergman spaces of infinite order are power bounded resp. uniformly mean ergodic.

This report defines the syntax and formal semantics of the Chi 2.0 formalism. The Chi formalism integrates concepts from dynamics and control theory with concepts from computer science, in particular from process algebra and hybrid automata. It combines a high expressivity and ease of modeling with a formal semantics. The Chi language is defined by means of an abstract and a concrete syntax. Th...

Program composition and compositional proof systems have proven them­ selves important for simplifying the design and the verification of programs. The paper presents a version of the jigsaw program composition operator pre­ viously defined in [FFG90, FFG91]. Here, the jigsaw operator is defined as the unification of its components by their most general unifier. The jigsaw operator generalizes ...