Calculus of Differential Operators

Abstract

This chapter is devoted to the theory of differentiation of — and differential operators acting on — functionals of white noise. On one hand the ideas are very much inspired by the work of P. Lévy (in particular Lévy (1951)), and on the other hand by the theory of creation and annihilation operators on Fock space (e.g., Berezin (1966)). Background references for this chapter are, Hida (1975a), Kubo and Takenaka (1980b), Kuo (1983d), Potthoff and Yan (1992), and for the general theory of Gâteaux and Fréchet derivatives, e.g., the book of Schwartz (1969).