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On an Inversion Formula for an Integral Transform of Convolution Type

On an Inversion Formula for an Integral Transform of Convolution Type
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The convolution of an extension of Al-Zughair integral transform

Journal of Interdisciplinary Mathematics, 2019
AbstractWe will introduce in this paper, a definition the convolution of an extension of Al-Zughair integral transform and properties and how to benefit from it to solve ordinary differential equat...
Ali Hassan Mohammed, Ameer Qassim Majde
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A Fourier generalized convolution transform and applications to integral equations

Fractional Calculus and Applied Analysis, 2012
An integral transform related to Fourier sine, Fourier cosine and generalized convolution is introduced and a Watson type theorem for the transform is proved. Later on, solutions of some integral equations in closed form are obtained as applications.
Nguyen Thanh Hong, Nguyen Xuan Thao, Tuan Vu Kim   +2 more
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Generalized integral transforms and convolution products on function space

Integral Transforms and Special Functions, 2011
In this paper, we use a Gaussian process to define a generalized integral transform (GIT) and a generalized convolution product (GCP) of functionals defined on a function space. We establish the existence and some properties for the GIT, the GCP and the inverse integral transform. Finally, we prove a Fubini theorem for the GIT and the GCP.
Hyun Soo Chung, Vu Kim Tuan
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Integral operators related to generalized convolutions for Hankel transform

Integral Transforms and Special Functions, 2009
The present research is devoted to integral transforms related to generalized convolutions, or polyconvolutions, for Hankel transform H ν[f](x). Two polyconvolutions with the factorization properties are considered in space . Existence conditions and boundary properties are found. Watson’s type theorems for convolution transforms are proved.
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Integral Transforms Related to a Generalized Convolution

Results in Mathematics, 2000
A general convolution transform of the Fourier cosine-sine type is investigated. The authors find necessary and sufficient conditions on the kernel function, which makes the mentioned transform a unitary transform on \(L_2(\mathbb{R})\). A special class of the Fourier sine kernels is defined. Watson and Plancherel type theorems are proved.
Al-Musallam, F., Tuan, Vu Kim
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A FUBINI THEOREM FOR INTEGRAL TRANSFORMS AND CONVOLUTION PRODUCTS

International Journal of Mathematics, 2013
In this paper we establish Fubini theorems for integral transforms and convolution products for functionals on function space.
Chung, Hyun Soo, Skoug, David, Chang, Seung Jun   +2 more
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Some inequalites for convolution integral transforms

Integral Transforms and Special Functions, 1994
In this paper we consider the inqualities for convolution integral transforms.We proceed to the study of the operators fractional integration and applications to the theory of integral equations.
Askhab Yakubov, Lamara Shankishvili
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Factorization of integral transformations of convolution type

Journal of Soviet Mathematics, 1985
Translation from Itogi Nauki Tekh., Ser. Mat. Anal. 21, 3-41 (Russian) (1983; Zbl 0562.44005).
Brychkov, Yu. A., Glaeske, H.-J., Marichev, O. I.   +2 more
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