- The dual space of A∞(Ω)

Throughout this book, when Ω is a bounded domain with C∞ boundary, we have singled out the space A∞(Ω) as a particularly nice subspace of whatever space of holomorphic functions on Ω we were studying. In this chapter, we will study A∞(Ω) for its own sake, and we will prove a representation theorem for linear functionals on this space. An example of a typical linear functional on A∞(Ω) is given by h 7→ h(n)(a) where a is any point in Ω and n is a positive integer.