δ-β-Gabor integral operators for a space of locally integrable generalized functions
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Date
2020
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Abstract
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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Keywords
Boehmian, Gabor Integral, Signal, Time-Frequency Integral, Window Function, Δ-Β-Gabor Integral, Artificial neural network, Gabor integral, Geometry, Space (punctuation), Mathematical analysis, Convolution (computer science), Time-frequency integral, Machine learning, QA1-939, FOS: Mathematics, Fourier integral operator, Advanced Techniques in Digital Signal Processing, Axiom, Signal, Integrable system, Algebra over a field, Convolution theorem, Applied Mathematics, δ-β-Gabor integral, Fractional Fourier Transform Analysis, Pure mathematics, Operator theory, Linguistics, Window function, Computer science, Fourier analysis, Fractional Fourier transform, FOS: Philosophy, ethics and religion, Philosophy, Physical Sciences, Computer Science, Signal Processing, Modulation Spaces, Fourier transform, FOS: Languages and literature, Boehmian, Computer Vision and Pattern Recognition, Image Denoising Techniques and Algorithms, Mathematics, Convolution as an integral transform, \(\delta\)-\(\beta\)-Gabor integral, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Special integral transforms (Legendre, Hilbert, etc.), Nontrigonometric harmonic analysis involving wavelets and other special systems, window function, Integral operators, time-frequency integral, Integral transforms in distribution spaces, signal
Fields of Science
01 natural sciences, 0101 mathematics
Citation
Al-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.
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Advances in Difference Equations
Volume
2020
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1
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