How difficult is it to get an assistant professor position in a department (e.g., applied math) while you have a PhD degree from another area (e.g., electrical engineering)? Particularly, when you target only relatively good departments (top 20~30).
If it makes any difference, I am particularly thinking of becoming professor of applied math with an EE degree.
update: I don't know exactly what constitutes mathematical research in the eyes of mathematicians, but I can say there are some really theoretical subjects needed in my research. For example random matrix theory and empirical processes are prevalent in my research area. However, in spite of my great interest, I haven't been able to (or prohibited from doing) work on purely theoretical part of the problems. So I mostly have applied the existing theoretical results. Developing optimization algorithms with provable convergence guarantees, perhaps in statistical sense of it, are also important in the area I worked in. However, I don't think optimization is considered an interesting area for mathematicians.