# Solving dual integral equations on Lebesgue spaces

Óscar Ciaurri; José Guadalupe; Mario Pérez; Juan Varona

Studia Mathematica (2000)

- Volume: 142, Issue: 3, page 253-267
- ISSN: 0039-3223

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topCiaurri, Óscar, et al. "Solving dual integral equations on Lebesgue spaces." Studia Mathematica 142.3 (2000): 253-267. <http://eudml.org/doc/216802>.

@article{Ciaurri2000,

abstract = {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.},

author = {Ciaurri, Óscar, Guadalupe, José, Pérez, Mario, Varona, Juan},

journal = {Studia Mathematica},

keywords = {Fourier series; Hankel transform; Bessel functions; dual integral equations; dual integral equations of Titchmarsh type; uniqueness; Jacobi polynomials; Fourier-Neumann series; convergence; almost everywhere convergence},

language = {eng},

number = {3},

pages = {253-267},

title = {Solving dual integral equations on Lebesgue spaces},

url = {http://eudml.org/doc/216802},

volume = {142},

year = {2000},

}

TY - JOUR

AU - Ciaurri, Óscar

AU - Guadalupe, José

AU - Pérez, Mario

AU - Varona, Juan

TI - Solving dual integral equations on Lebesgue spaces

JO - Studia Mathematica

PY - 2000

VL - 142

IS - 3

SP - 253

EP - 267

AB - 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.

LA - eng

KW - Fourier series; Hankel transform; Bessel functions; dual integral equations; dual integral equations of Titchmarsh type; uniqueness; Jacobi polynomials; Fourier-Neumann series; convergence; almost everywhere convergence

UR - http://eudml.org/doc/216802

ER -

## References

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