Let L be a linear differential operator, and let f be a smooth function with compact support K. Is there a solution to the equation Lu = f? The answer is "no" in general, but the answer to a related question is often "yes." The related question is, does there exist a function g, for which g restricted to K equals f, and for which there is a solution to the equation Lu = g?

In this talk I will give some beginning hints about how noncommutative harmonic analysis (representation theory) can be used to show that the answer to the second question is "yes" for certain left-invariant differential operators on Lie groups.

DE/Geom/Top Seminar main page