Survey of recent developments on the Pompeiu problem and the Schiffer problem. This problem has surprising interactions with inverse scattering, image processing and other applied problems.
Lecture presented at Taniguchi Symposium, Katata, June 1995. Deals with new kind of differential equations for multivalued functions. The monodromy operator is allowed to enter into the equation. Related to resurgence and complex dynamics.
Lecture delivered at Research Institute for Mathematical Sciences, Kyoto University, Symposium on Algebraic Analysis, July 1995. Explains the relationship between new kinds of D-modules and ideals of exponential polynomials.
