New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type |
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| Authors: | Luis P. Castro Rita C. Guerra Nguyen Minh Tuan |
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| Affiliation: | 1. Center for Research and Development in 2. Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Aveiro, Portugal;3. Department of Mathematics, College of 4. Education, Viet Nam National University, Hanoi, Viet Nam |
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| Abstract: | We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained. |
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| Keywords: | convolution factorization Fourier integral operator Hankel operator integral equation Wiener-Hopf operator |
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