I know only a little bit about C$^*$-algebras and I want a to know if you know a nice apllication or the influence of them in the field of partial differential equations (it is better that it is understandable for graduate students), or maybe can explain me why they are important for pseudo-differential-operators. A similar question i found here http://math.stackexchange.com/questions/798342/application-of-calgebras but there are not enough answers to convince me. I'm not sure if it is ok to ask it here, but maybe anyone could know more about C$^*$-algebras and partial differential equations. Regards