The boundedness of the weighted differentiation composition operator from the logarithmic Bloch space to the weighted-type space is characterized in terms of the sequence (zn)n∈N0 . An asymptotic estimate of the essential norm of the operator is also given in terms of the sequence, which gives a characterization for the compactness of the operator.

The current on a linear strip or wire solves an equation governed by a linear integraldifferential operator that is the composition of the Helmholtz operator and an integral operator with logarithmically singular displacement kernel. We investigate the spectral behavior of this classical operator, particularly because various methods of analysis and solution rely on asymptotic properties of spe...

Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcal{H}(Omega_X)$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcal{A}^omega(Omega_X)$ is the space of all $finmathcal{H}(Omega_X)$ for which $$|f(x)|leqslant C omega(r_{Omega_X}(x)),quad xin Omega_X,$$ for some constant $C>0$, whenever $r_{Omega_X}$ is the M...

In the present paper we study a relation between the Lorentzian twistor equation and CR-geometry. Besides the Dirac operator there is a second important conformally covariant differential operator acting on the spinor fields Γ(S) of a smooth semiRiemannian spin manifold (M,g) of dimension n and index k, the so-called twistor operator D. The twistor operator is defined as the composition of the ...

The paper contains a new prof for the sufficiency in Joel H. Shapiro’s recent characterization of inner functions saying that an analytic selfmap φ of the open unit disk is an inner function if and only if the essential norm of the composition operator of symbol φ is equal to √ 1+|φ(0)| 1−|φ(0)| . The main ingredient in the proof is a formula for the essential norm of a composition operator in ...

In this paper we study weighted composition operators on Orlicz spaces. Introduction : Let X and Y be two non empty sets and let F(X) and F(Y) be denoted the topological vector spaces of complex valued functions on X and Y respectively. If T : Y → X is a mapping such that f oT ∈ F (Y) whenever f ∈ F (X), then we can define a composition transformation C T : F (X) → F (Y) by C T f = f oT for eve...

An operator for the composition of two processes, where one process has priority over the other process, is studied. Processes are described by action systems, and data refinement is used for transforming processes. The operator is shown to be compositional, i.e. monotonic with respect to refinement. It is argued that this operator is adequate for modelling priorities as found in programming la...

Let C , be a composition operator on L (A). Some conditions under which C, is an isometry and Hermitian are investigated in this paper. Some study of normal composition operators is also made.