Abstract
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 , ∞ ) 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.
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