Solving dual integral equations on Lebesgue spaces
Studia Mathematica, Tome 142 (2000) no. 3, pp. 253-267
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.
Keywords:
Fourier series, Hankel transform, Bessel functions, dual integral equations
@article{10_4064_sm_142_3_253_267,
author = {\'Oscar Ciaurri and Jos\'e Guadalupe and Mario P\'erez and Juan Varona},
title = {Solving dual integral equations on {Lebesgue} spaces},
journal = {Studia Mathematica},
pages = {253--267},
year = {2000},
volume = {142},
number = {3},
doi = {10.4064/sm-142-3-253-267},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-142-3-253-267/}
}
TY - JOUR AU - Óscar Ciaurri AU - José Guadalupe AU - Mario Pérez AU - Juan Varona TI - Solving dual integral equations on Lebesgue spaces JO - Studia Mathematica PY - 2000 SP - 253 EP - 267 VL - 142 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-142-3-253-267/ DO - 10.4064/sm-142-3-253-267 LA - en ID - 10_4064_sm_142_3_253_267 ER -
%0 Journal Article %A Óscar Ciaurri %A José Guadalupe %A Mario Pérez %A Juan Varona %T Solving dual integral equations on Lebesgue spaces %J Studia Mathematica %D 2000 %P 253-267 %V 142 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4064/sm-142-3-253-267/ %R 10.4064/sm-142-3-253-267 %G en %F 10_4064_sm_142_3_253_267
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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