A β-Convolution Theorem Associated with the General Quantum Difference Operator. (24th February 2022) - Shehata, Enas M.; El Zafarani, Rasha M.
Abstract : In this paper, we prove some properties of the β -partial derivative. We define the β -convolution of two functions associated with the general quantum difference operator, D β f t = f β t − f t / β t − t ; β is a strictly increasing continuous function. Moreover, we study the shift, the associative law, and the β -differentiability of the β -convolution. Furthermore, we prove the β -convolution theorem and give some applications.