Quantum white noise convolution operators with application to differential equations

Abstract

In this paper we introduce a quantum white noise (QWN) convolution calculus over a nuclear algebra of operators. We use this calculus to discuss new solutions of some linear and non-linear di erential equations.

The q-Gamma White Noise

“…Also a space of holomorphic functions on the complexification of E α,q with θ-exponential growth which is the analogue of the Gaussian case (where θ is the Young function) can be introduced. We expect to develop a new quantum q-Gamma white noise operator theory as an analogue of the quantum white noise operator theory, (see [2]- [6], [11]- [13]). …”

Operator theory: quantum white noise approach

“…In this section, we summarize the common notations and concepts used throughout the paper which can be found in Refs. [5][6][7]10,19,21,23,24,28,29].…”