New convolutions and their applicability to integral equations of Wiener‐Hopf plus Hankel type

摘要

>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.