ABSTRACT
This chapter discusses the links between some new results in the theory of infinite order differential operators on hyperfunctions and some very classical theories of Fantappie. More specifically, while it is well known the link between Fantappie’s analytic functionals and hyperfunction theory, it is not so widespread the knowledge that the same algebraic and topological techniques which have led to hyperfunctions, can be used to provide some interesting extensions of Fantappie’s theory. The chapter explores the case of analytic functionals in several variables. In this case, the theory of Fantappie was far from being complete, in view of the different topological structure of singularities which several complex variables functions have, when compared with one complex variable functions. The chapter also describes Martineau’s precise treatment of Fantappie’s theory, with a focus on Martineau’s foundations of the theory of the antisymmetric indicatrix.
