The Hypergeometric Approach to Integral Transforms and Convolutions
1994Preface. 1. Preliminaries. 2. Mellin Convolution Type Transforms with Arbitrary Kernels. 3. H- and G-Transforms. 4. The Generalized H- and G-Transforms. 5. The Generating Operators of Generalized H-Transforms. 6. The Kontorovich--Lebedev Transform. 7. General W-Transform and its Particular Cases. 8.
Semen B. Yakubovich, Yurii F. Luchko
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A general class of integral transforms and an expression for their convolution formulas
Integral Transforms and Special Functions, 2021A class of integral transforms which satisfies certain assumptions is considered. Several examples, including the Fourier, Laplace and Mellin transforms, are in this class as well as transforms whi...
Thomas Futcher, Marianito R. Rodrigo
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Composition method for constructing convolutions for integral transforms
Integral Transforms and Special Functions, 1996The composition method for constructing convolutions for integral transforms are given. Several original convolutions are described for transforms of Fourier type.
V.A. Kakichev +2 more
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THE DISCRETE FOURIER TRANSFORM AND CYCLIC CONVOLUTION ON INTEGRAL LATTICES
Mathematics of the USSR-Sbornik, 1989zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalized convolutions for the Fourier integral transforms and applications
2008Summary: This paper provides some generalized convolutions for the Fourier integral transforms and treats the applications. Namely, there are six generalized convolutions with weight-function for the Fourier integral transforms. As for applications, the normed ring structures on \(L^1(\mathbb{R}^d)\) are constructed, and the explicit solution in \(L^1(\
Bui Thi Giang, Nguyen Minh Tuan
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Images Classification Integrating Transformer with Convolutional Neural Network
Advances in Engineering Technology Research, 2023Convolutional neural networks (CNN) are one of the most widely used deep learning methods in computer vision, which can effectively extract local spatial information from images, but lack global understanding and dependency modelling of image features. As a result, contextual information cannot be fully utilized by the network.
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Integrating Convolution and Transformer for Enhanced Diabetic Retinopathy Detection
International Journal of Bio-Inspired Computation, 2023Xinrong Cao +3 more
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Sumudu transform and the solution of integral equations of convolution type
International Journal of Mathematical Education in Science and Technology, 2001The convolution theorem for the Sumudu transform of a function which can be expressed as a polynomial or a convergent infinite series is proved and its applicability demonstrated in solving convolution type integral equations.
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A note on convolution theorem for some integral transforms
AIP Conference Proceedings, 2023Deepika Jain +3 more
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A class of integral transforms related to the fourier cosine convolution
Integral Transforms and Special Functions, 2005In this work the class of integral transforms related to the Fourier cosine convolution is studied on L 2(R +). Watson’s type theorem is proved. The concept of the symmetric Fourier cosine kernel with a characteristic polynomial is defined. Plancherel’s theorem is formulated. The integral transforms with unsymmetric kernels are studied.
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