Baleanu, DumitruAl-Omari, Shrideh KhalafBaleanu, DumitruNisar, Kottakkaran Sooppy2023-02-132023-02-132020Al-Omari, Shrideh Khalaf...et al. (2020). "δ-β-Gabor integral operators for a space of locally integrable generalized functions", Advances in Difference Equations, Vol. 2020, No. 1.1687-1839https://hdl.handle.net/20.500.12416/6218In 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.eninfo:eu-repo/semantics/openAccessBoehmianGabor IntegralSignalTime-Frequency IntegralWindow FunctionΔ-Β-Gabor IntegralArticle2020110.1186/s13662-020-02961-x