The rank of Hankel operators on harmonic Bergman spaces

We show that on the harmonic Bergman spaces, the Hankel operators with nonconstant harmonic symbol cannot be of finite rank.

     

Tools for resource-constrained project scheduling and control: forward and backward slack analysis

Project managers generally consider slack as a measure of the scheduling flexibility associated with the activities in the project network. Nevertheless, when resource constraints appear, this information must be calculated and analysed carefully. In this context, to handle project feasible schedules is very hard work for project managers. In order to develop useful tools for decision making, the authors extend the concepts of activity slack and define a new activity criticality index based on them that permits us to classify the activities in the resource-constrained project scheduling and control context. Additionally, these new concepts have been integrated into standard project management software as new commands. Hence the capabilities of project management software are improved. Finally, an example that illustrates the use and application of the new activity classification is also included.     

On Toeplitz operators with quasihomogeneous symbols

In this paper, we give some basic results concerning Toeplitz operators whose symbol is of the form e^{i p θ}ϕ, where ϕ is a radial function, then use these results to characterize all Toeplitz operators which commute with them.Received: 12 June 2004; revised: 27 January 2005     

Quasihomogeneous Toeplitz operators on the harmonic Bergman space

In this paper we study the product of Toeplitz operators on the harmonic Bergman space of the unit disk of the complex plane \mathbbC{\mathbb{C}}. Mainly, we discuss when the product of two quasihomogeneous Toeplitz operators is also a Toeplitz operator, and when such operators commute.     

Products of Toeplitz Operators on the Bergman Space

In 1962 Brown and Halmos gave simple conditions for the product of two Toeplitz operators on Hardy space to be equal to a Toeplitz operator. Recently, Ahern and Cucković showed that a similar result holds for Toeplitz operators with bounded harmonic symbols on Bergman space. For general symbols, the situation is much more complicated. We give necessary and sufficient conditions for the product to be a Toeplitz operator (Theorem 6.1), an explicit formula for the symbol of the product in certain cases (Theorem 6.4), and then show that almost anything can happen (Theorem 6.7).