Duality Theory for Spaces of Germs and Holomorphic Functions on Nuclear Spaces

Abstract

Publisher Summary This chapter presents a study on the duality theory for spaces of germs and holomorphic functions on nuclear spaces. The chapter presents a continuation on the study of holomorphic functions, defined on open subsets of ceratin nuclear locally convex spaces. The directions developed in the chapter are quite varied, but in fact are natural consequences of the approaches initiated. The chapter discusses A-nuclear spaces. The basic defining property of A-nuclear spaces first arose in a theorem. A-nuclear spaces were initially defined to show that certain spaces of holomorphic functions and analytic functionals were nuclear. In this chapter, various topological vector space properties of A-nuclear spaces are proved and applied to improve and simplify results. The chapter also presents examples of a move towards a more unified theory and of a bornological space.