Mathematical analysis and computational complexity? computational complexity involves large amounts of Combinatorics and number theory, some ingridiences from stochastics, and an emerging amount of algebra.

However, being a analysist, I wonder whether there are applications of analysis into this field, or maybe ideas inspired by analysis. All I know which slightly corresponds to this is the Fourier transform on Finite groups.

Can you help me?
Flajolet and Sedgewick published the book "Analytic Combinatorics" http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html.  I don't know much about that topic, but people in the field use tools from complex analysis.  So far, their applications seem more on analysis of algorithms, not on computational complexity, as far as I see.