PIs Geronimo and Woerdeman will continue their investigations into factorization and extension problems. In particular we hope to develop a constructive proof of the celebrated Ferguson-Lacey extension theorem and build on it using the results we have recently obtained on the spectral factorization of positive two variable trigonometric polynomials. We plan to investigate in more detail fast algorithms for computing the structured matrices that arise from the two variable trigonometric moment problem as well as study the orthogonal polynomials that arise in this case. The PIs also plan to continue their individual investigation into the important problems arising from quantum computing and the asymptotics of solutions to 2nd order difference equations.
The types of structured matrices under study here arise in many problems of practical interest such as two variable auto-regressive models and two variable filtering. The PIs will try to recruit more undergraduate and graduate students to help in these problems as well as give courses and lectures at conferences to increase the impact of their efforts. In order to make the intellectual merit of the proposal apparent the PIs will continue to publish their results in well respected journals, and also disseminate them via the PIs' homepages, preprint servers such as arXiv, software sharing websites, etc.
