ABSTRACT
Using the Poisson integral representation of the normalized Bessel function }a(kx) studied in Chapter 1, J. Delsarte has defined in [21] the Poisson transform
by
Where f is a continuous function on [0, + »[. J.L.Lions has considered in [57] the operator J l a . He has called it Delsarte
operator, and has proved that it is a transmutation operator of the Bessel operator
given by
whereinto
The transform has been called in [83] Riemann-Liouville integral transform.
