The research conducted by the members of the analysis section, covers a broad area ranging from complex analysis to function theory in several complex variables, differential equations, the theory of operator algebras, real function theory, representation theory and probability theory. Every area consists of a number of subjects, e.g.: the area of differential equations is, roughly, divided into the fields of linear partial differential equations, non-linear partial differential equations, integrable systems, inverse problems, etc. The research carried out in the mathematical analysis section can also be classified from the point of view of the methods involved. These include : the complex analysis method, the real analysis method including the method of singular integral operators, micro-local analysis and the method of algebraic analysis originated by Mikio Sato, the functional analysis method in the tradition of Tosio Kato and Kôsaku Yosida, the non-linear analysis method including the variational method and that due to the fixed point theorem or the probabilistic method including the stochastic differential equation after Kiyosi Itô. In many cases, these would of course be combined in our investigations of problems in mathematical analysis.

There are sixteen members working in mathematical analysis : nine professors and seven associated professors. The above classification of research areas, however, cannot be strict ; there are at least three or four more faculty members who are working in related research subjects. For more detailed information on the research in mathematical analysis conducted by individual members we refer to the list of faculty members.