Xiaojing Lyu
We study the interplay between analysis on manifolds with singularities and complex analysis and develop new structures of operators based on the Mellin transform and tools for iterating the calculus for higher singularities. We refer to the idea of interpreting boundary value problems (BVPs) in terms of pseudo-differential operators with a principal symbolic hierarchy, taking into account that BVPs are a source of cone and edge operator algebras. The respective cone and edge pseudo-differential algebras in turn are the starting point of higher corner theories. In addition there are deep relationships between corner operators and complex analysis. This will be illustrated by numerous examples.
