If φ is an analytic map of the unit diskD into itself, the composition operator Cφ on the Hardy space H (D) is defined by Cφ(f) = f ◦ φ. For a certain class of composition operators with multivalent symbol φ, we identify a subspace of H(D) on which C∗ φ behaves like a weighted shift. We reproduce the description of the spectrum found in [5] and show for this class of composition operators that ...

A comparative study of weighted residual methods has been made on different types of advection diffusion equations. Both the linear and non-linear models have been discretized by orthogonal collocation method (OCM) and orthogonal collocation on finite elements (OCFE). Model equations have been solved by MATLAB ‘ode15s’ system solver. Numerical values have been compared with analytic ones and in...

We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form (1− 〈z, w〉)−γ for γ > 0. We find necessary and sufficient conditions for the adjoint of a weighted composition operator to be a weighted composition operator or the inverse of a weighted composition operator. We then obtain characterizations of self-adjoint and unitary weigh...

The number of isolated intersections between a smooth curve in Eu-clidean space and an arbitrary hyperplane can be majorized by a weighted sum of integral Frenet curvatures of the curve. In the complex Hermitian space one can derive a similar result for holomorphic curves but with much better weights. The proof of this result is based on a generalizationof the Milnor{FF ary theorem for complex ...

Let H D denote the space of all analytic functions in the open unit disc D of the finitecomplex plane C, ∂D the boundary of D, N0 the set of all nonnegative integers and N the set of all positive integers. Let μ z be a positive continuous function on D weight such that μ z μ |z| and n ∈ N0. The nth weighted-type spaces on the unit disk D, denoted by W n μ D which were introduced in 1 , consist ...

We extend a classical result of Caughran/H. Schwartz and another recent result of Gunatillake by showing that if D is a bounded, convex domain in C, ψ : D → C is analytic and bounded away from zero toward the boundary of D, and φ : D → D is a holomorphic map such that the weighted composition operator Wψ,φ is compact on a holomorphic functional Hilbert space (containing the polynomial functions...