Algebraic properties of Mehler–Fock convolution and applications.

In this paper, we study some properties of the Mehler–Fock convolution operator. We also analyse the Banach algebraic structure on the space of integrable functions $ L_1(1,\infty) $ L 1 (1 , ∞) with the multiplication being the Mehler–Fock convolution. The Titchmarsh-type theorem for this convolution operator is also obtained. As applications, we apply these properties of the convolution operator to solve some classes of Fredholm integral and integro-differential equations and prove some priori estimations under the given conditions. [ABSTRACT FROM AUTHOR]