Geodesic
Solving dual integral equations on Lebesgue spaces
Studia Mathematica, Tome 142 (2000) no. 3, pp. 253-267

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $∑_{n=0}^{∞} c_n J_{μ+2n+1}$ 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.
DOI : 10.4064/sm-142-3-253-267
Keywords: Fourier series, Hankel transform, Bessel functions, dual integral equations

Óscar Ciaurri 1 ; José Guadalupe 1 ; Mario Pérez 1 ; Juan Varona 1

1 
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Óscar Ciaurri; José Guadalupe; Mario Pérez; Juan Varona. Solving dual integral equations on Lebesgue spaces. Studia Mathematica, Tome 142 (2000) no. 3, pp. 253-267. doi: 10.4064/sm-142-3-253-267

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