Fourier-type algebras and applications to some classes of convolution-type integral equations

This work presents three new Fourier-type Banach algebras generated by the distinct convolution multiplications. In particular, the first algebra is based on the Hartley convolution. For the second and third algebras, a main ingredient is the appropriate use of a group of four previously constructed convolutions associated with the Fourier-cosine and Fourier-sine integral transforms defined on the whole space $\mathbb{R}^{d}$ and half-axis $\mathbb{R}^{+}$ , respectively. With the practical problems, Sect. 3 considers the applications for two large enough classes of the integral equations. Namely, the solvability of the equations is completely investigated, and the explicit solutions are obtained. With respect to approximate computations in the practical problems, every solution can be expressed in terms of a Neumann functional series, and of course, they belong to the constructed algebra.