ITR: Analysis of the Capacity Improvement for Wireless Networks with Multiple Transmit and Receive Antennas

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It is very well known that there is sometimes a striking divergence between the continuous and the discrete. The theory of time scales has been initiated by Stefan Hilger ten years ago in order to unify study for differential and difference equations. Not only is it able to treat these two cases simultaneously, but it also can handle numerous other cases \in between" the continuous and the discrete, and those cases might be important for applications. For this reason it also could be worth to think about the consequences of a better developed time scales theory for graduate and in particular for undergraduate education. As the theory is very new and virtually important to every area in analysis, work on this subject done now will be fundamental. If NSF funds this proposal we would expand the theory of dynamic equations on time scales in various ways. We would like to conduct study of linear dynamic systems on time scales which would result in a better understanding of higher order dynamic equations. For those the task of characterizing disconjugacy is an interesting one, and this question we also want to address for higher order Sturm-Liouville dynamic equations or, more general, linear Hamiltonian dynamic systems on time scales. Such systems also would beinteresting if an eigenvalue parameter was involved, and we would like to derive an existence theorem, an expansion theorem, Rayleigh's Principle, and more general oscillation results for these eigenvalue problems. Another interesting task, which is intimately connected to the above problems, would be to establish a theory of variational analysis on time scales. To give necessary and sufficient conditions for strong and weak local minima would be the main concern of such a project, and it would also be of use to establish a Weierstrab Theory for variational problems on time scales.