Baleanu, DumitruAl-Omari, Shrideh KhalafBaleanu, DumitruNisar, Kottakkaran Sooppy2022-03-312022-03-312020Al-Omari, Shrideh Khalaf; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy (2020). "delta-beta-Gabor integral operators for a space of locally integrable generalized functions", Advances in Difference Equations, Vol. 2020, No. 1.https://hdl.handle.net/20.500.12416/5229In this article, we give a definition and discuss several properties of the delta-beta -Gabor integral operator in a class of locally integrable Boehmians. We derive delta sequences, convolution products and establish a convolution theorem for the given delta-beta -integral. By treating the delta sequences, we derive the necessary axioms to elevate the delta-beta -Gabor integrable spaces of Boehmians. The said generalized delta-beta -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/openAccessΔ-Β-Gabor IntegralTime-Frequency IntegralSignalGabor IntegralBoehmianWindow FunctionArticle2020110.1186/s13662-020-02961-x