δ-β-Gabor integral operators for a space of locally integrable generalized functions

被引：0
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作者：
Shrideh Khalaf Al-Omari
Dumitru Baleanu
Kottakkaran Sooppy Nisar
机构：
[1] Al-Balqa Applied University,Department of Physics and Basic Sciences, Faculty of Engineering Technology
[2] Cankaya University,Department of Mathematics
[3] Prince Sattam Bin Abdulaziz University,Department of Mathematics, College of Arts and Sciences
来源：
Advances in Difference Equations | / 2020卷
关键词：
-; -Gabor integral; Time-frequency integral; Signal; Gabor integral; Boehmian; Window function; 54C40; 14E20; 46E25; 20C20;
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摘要：
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.
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