In this article, we give a definition and discuss several properties of the δ-β-Gabor integral operator in a class of locally integrable Boehmians. We derive delta sequences, convolution products and establish a convolution theorem for the given δ-β-integral. By treating the delta sequences, we derive the necessary axioms to elevate the δ-β-Gabor integrable spaces of Boehmians. The said generalized δ-β-Gabor integral is, therefore, considered as a one-to-one and onto mapping continuous with respect to the usual convergence of the demonstrated spaces. In addition to certain obtained inversion formula, some consistency results are also given.

在本文中，我们给出了一个定义，并讨论了在一类局部可积分的Boehmian中δ - β- Gabor积分算子的几个性质。我们导出增量序列，卷积积，并为给定的δ - β-积分建立卷积定理。通过处理增量序列，我们得出了必要的公理，以提升波希米亚人的δ - β- Gabor可积空间。所述广义δ - β因此，-Gabor积分被认为是一对一的，并且相对于所展示空间的通常收敛性而言，映射是连续的。除了获得一定的反演公式外，还给出了一些一致性结果。