C*-operator algebras allow us to extend many of the computational techniques developed for matrices to infinite-dimensional space -- including methods for control and optimization of state-space systems. In this talk, we discuss several classes of parameterized C*-operator algebras, with a particular focus on the algebra of Partial Integral (PI) operators -- an algebra which can be characterized using multiplier operators or integral operators with semi-separable kernels. Specifically, we show that solutions of linear PDE can be represented using Partial Integral Equations (PIEs) -- a form of dynamic system parameterized by PI operators. We place an emphasis on unsolved problems involving PI operators, focusing in particular on the problem of testing positivity of a PI operator. Finally, we briefly describe PIETOOLS, a Matlab toolbox interface which allows for the manipulation and optimization of PI operators.
Our C*-Seminar will still (as it was last year) be on Wednesdays, but the time will now be a bit different: 1:30-2:45 pm (Arizona time, no daylight savings), meeting both in person (WXLR A309) and via zoom.
Also new: it's now the ASUERAU C*-Seminar (so, joint with our friends Lara and Mitch at Embry-Riddle Aeronautical University up the road in Prescott).
(Please email the organizer John Quigg quigg@asu.edu to be put on the email list if you would like to receive the link to the zoom seminar.)
Matthew Peet
Associate Professor of Aerospace Engineering
Department of Mechanical and Aerospace Engineering
Arizona State University