A Convolution Operator Related to the Generalized Mehler–Fock and Kontorovich–Lebedev Transforms
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In this paper we study a generalization of an index integral involving the product of modified Bessel functions and associated Legendre functions. It is applied to a convolution construction associated with this integral, which is related to the classical Kontorovich–Lebedev and generalized Mehler–Fock transforms. Mapping properties and norm estimates in weighted L p -spaces, 1 ≤ p ≤ 2, are investigated. An application to a class of convolution integral equations is considered. Necessary and sufficient conditions are found for the solvability of these equations in L 2.
Mathematics Subject Classification (2000)44A15 44A05 44A35 33C10 45A05
KeywordsKontorovich–Lebedev transform Generalized Mehler–Fock transform Modified Bessel function associated Legendre functions convolution integral equations index integrals
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