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Solving dual integral equations on Lebesgue spaces

Óscar Ciaurri, José Guadalupe, Mario Pérez, Juan Varona (2000)

Studia Mathematica

We study dual integral equations associated with Hankel transforms, that is, dual integral equations of Titchmarsh’s type. We reformulate these equations giving a better description in terms of continuous operators on L p spaces, and we solve them in these spaces. The solution is given both as an operator described in terms of integrals and as a series n = 0 c n J μ + 2 n + 1 which converges in the L p -norm and almost everywhere, where J ν denotes the Bessel function of order ν. Finally, we study the uniqueness of the solution....

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