Quantum white noise Tricomi equation

Abstract

It is well known that every white noise operator admits an infinite series expansion in terms of integral kernel operators and, therefore, is considered as a function of the annihilation operator and creation operator. This gives a natural idea for studying the quantum white noise counterpart of the Tricomi equation by replacing the real variables \(x\) and \(y\) by the non-commutative variables annihilation operator and creation operator. Based on an infinite-dimensional test space of holomorphic functions, the solutions are shown to be linear continuous operators.