We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces Bα of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they grow at least exponentially, and this speed of convergence is only obtained for symbols which do not approach the unit circle. We also give an upper bounds and explicit an example. Mathematics Su...

Let Dn be the unit polydisc of Cn. The class of all holomorphic functions with domain Dn will be denoted by H(Dn). Let φ be a holomorphic self-map of Dn, the composition operator Cφ induced by φ is defined by (Cφ f )(z) = f (φ(z)) for z ∈Dn and f ∈H(Dn). If, in addition, ψ is a holomorphic function defined on Dn, the weighted composition operator ψCφ induced by ψ and φ is defined by ψCφ(z) = ψ(...

An approximation Ansatz for the operator solution, U(z′, z), of a hyperbolic first-order pseudodifferential equation, ∂z +a(z, x, Dx) with Re(a) ≥ 0, is constructed as the composition of global Fourier integral operators with complex phases. An estimate of the operator norm in L(H, H) of these operators is provided which allows to prove a convergence result for the Ansatz to U(z′, z) in some So...

In this paper, we study two types of the reducing subspaces for the weighted composition operator $W: frightarrow ucdot fcirc varphi$ on $L^2(Sigma)$. A necessary and sufficient condition is given for $W$ to possess the reducing subspaces of the form $L^2(Sigma_B)$ where $Bin Sigma_{sigma(u)}$. Moreover, we pose some necessary and some sufficient conditions under which the subspaces of the form...

Given a weight in , and a Young function , we consider the weighted modular ( ( )) ( ) and the resulting weighted Orlicz space ( ). For a Young function ∆ ( ) we present a necessary and sufficient conditions in order that ( ) = ( ) up to the equivalence of norms. We find a necessary and sufficient condition for in order that there exists an unbounded weight such that the above equality of space...

We develop a notion of spatial-behavioral typing suitable to discipline concurrent interactions and resource usage in distributed object systems. Our type structure reflects a resource sensitive model, where a parallel composition type operator expresses resource independence, a sequential composition type operator expresses resource synchronization, and a typemodality expresses resource owners...

A new model composer is proposed to automatically generate non-anonymous model replicas in the context of performability and dependability evaluation. It is a state-sharing composer that extends the standard anonymous replication composer in order to share the state of a replica among a set of other specific replicas or among the replica and another external model. This new composition operator...

An analytic self-map φ : D → D of the open unit disk D in the complex plane induces the composition operator Cφ on H(D), the space of holomorphic functions on D, defined by Cφ(f) = f ◦φ. A basic goal in the study of composition operators is to relate function theoretic properties of φ to operator theoretic properties of Cφ. Here we review some results that characterize when φ induces a bounded ...

Let ζ and η be distinct points on the unit circle and suppose that φ is a linear-fractional self-map of the unit disk D, not an automorphism, with φ(ζ) = η. We describe the C-algebra generated by the associated composition operator Cφ and the shift operator, acting on the Hardy space on D.

We prove that a composition operator is bounded on the Hardy space H of the right half-plane if and only if the inducing map fixes the point at infinity non-tangentially, and has a finite angular derivative λ there. In this case the norm, essential norm, and spectral radius of the operator are all equal to √ λ.