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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]

In this paper, we express the scattered Debye potentials via a new generalized convolution related to the Kontorovich-Lebedev integral. The uniform asymptotics of the scattered Debye potentials under very mild conditions on spectral functions are obtained, and an inverse problem of finding spectral functions from given Debye potentials is considered. [ABSTRACT FROM AUTHOR]