We study when a weighted composition operator acting between different weighted Bergman spaces is bounded, resp. compact.

A composition operator Tbf = f o b is completely continuous on H1 if and only if \b\ < 1 a.e. If the adjoint operator Tg is completely continuous on VMOA , then 7¿ is completely continuous on Hl . Examples are given to show that the converse fails in general. Two results are given concerning the relationship between the complete continuity of an operator and of its adjoint in the presence of ce...

* Correspondence: [email protected]. cn Department of Mathematics, Harbin Institute of Technology Harbin 150001, P.R.China Full list of author information is available at the end of the article Abstract We establish the Poincaré-type inequalities for the composition of the LaplaceBeltrami operator and the Green’s operator applied to the solutions of the nonhomogeneous A-harmonic equation in the Joh...

In this article, we first prove Orlicz norm inequalities for the composition of the homotopy operator and the projection operator acting on solutions of the nonhomogeneous A-harmonic equation. Then we develop these estimates to L (μ)averaging domains. Finally, we give some specific examples of Young functions and apply them to the norm inequality for the composite operator. 2000 Mathematics Sub...

We study an infinite population model for the genetic algorithm, where the iteration of the algorithm corresponds to an iteration of a map G. The map G is a composition of a selection operator and a mixing operator, where the latter models effects of both mutation and crossover. We examine the hyperbolicity of fixed points of this model. We show that for a typical mixing operator all the fixed ...

Let H(B) be the space of all holomorphic functions on the unit ball B in CN , and S(B) the collection of all holomorphic self-maps of B . Let φ ∈ S(B) and g ∈ H(B) with g(0) = 0 , the generalized composition operator is defined by C φ ( f )(z) = ∫ 1 0 R f (φ(tz))g(tz) dt t , Here, we characterize the boundedness and compactness of the generalized composition operator acting from Bloch-type spac...

Process algebras are suitable for describing networks of communicating processes. In most process algebras, the description of such networks is achieved using parallel composition operators. Noticing that the parallel composition operators commonly found in process algebras are often limited in expressiveness and/or difficult for novice users, we propose a new parallel operator that allows netw...

A holomorphic self-map φ of the unit disk is constructed such that the composition operator induced by φ is bounded on the Hardy-Sobolev space H1 2 of order 2 as well as on the ordinary holomorphic Lipschitz space Lip1 but unbounded on the Zygmund class Λ1. Among these three function spaces we have embedding relations H1 2 ⊂ Lip1 ⊂ Λ1. So, the main points here are that our construction provides...

In this paper, a genetic algorithm for making music compositions is presented. Position based representation of rhythm and relative representation of pitches, based on measuring relation from starting pitch, allow for a flexible and robust way for encoding music compositions. This approach includes a pre-defined rhythm applied to initial population, giving good starting solutions. Modified gene...

The analysis and design of hybrid systems must exploit their hierarchical and compositional nature of in order to tackle complexity. In previous work, we presented a hierarchical abstraction framework for hybrid control systems based on the notions of simulation and bisimulation. In this paper, we build upon our previous work and investigate the compositionality of our abstraction framework. We...