Euler’s Theorem for Homogeneous White Noise Operators

Abstract

In this paper we introduce a new notion of λ −order homogeneous operators on the nuclear algebra of white noise operators. Then, we give their Fock expansion in terms of quantum white noise (QWN) fields \(\{a_{t},\: a^{*}_{t}\, ; \; t\in \mathbb {R}\}\). The quantum extension of the scaling transform enables us to prove Euler’s theorem in quantum white noise setting.