On the Hartley – Fourier sine generalized convolution |
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| Authors: | Nguyen Xuan Thao Hoang Thi Van Anh |
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| Affiliation: | 1. Department of Mathematics, School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, , Hanoi, Vietnam;2. Department of Mathematics, Food Industry College, , PhuTho, Vietnam |
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| Abstract: | In this paper, we construct and study a new generalized convolution (f * g)(x) of functions f,g for the Hartley (H1,H2) and the Fourier sine (Fs) integral transforms. We will show that these generalized convolutions satisfy the following factorization equalities: ![urn:x-wiley:1704214:media:mma2980:mma2980-math-0001]( "urn:x-wiley:1704214:media:mma2980:mma2980-math-0001") We prove the existence of this generalized convolution on different function spaces, such as  . As examples, applications to solve a type of integral equations and a type of systems of integral equations are presented. Copyright © 2013 John Wiley & Sons, Ltd. |
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| Keywords: | Hartley Fourier cosine and Fourier sine transforms convolution generalized convolution integral equations |
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