  We study a non linear regression model with functional data as inputs and
scalar response. We propose a pointwise estimate of the regression function
that maps a Hilbert space onto the real line by a local linear method. We
provide the asymptotic mean square error. Computations involve a linear inverse
problem as well as a representation of the small ball probability of the data
and are based on recent advances in this area. The rate of convergence of our
estimate outperforms those already obtained in the literature on this model.
