  This paper presents a general notion of Mahalanobis distance for functional
data that extends the classical multivariate concept to situations where the
observed data are points belonging to curves generated by a stochastic process.
More precisely, a new semi-distance for functional observations that generalize
the usual Mahalanobis distance for multivariate datasets is introduced. For
that, the development uses a regularized square root inverse operator in
Hilbert spaces. Some of the main characteristics of the functional Mahalanobis
semi-distance are shown. Afterwards, new versions of several well known
functional classification procedures are developed using the Mahalanobis
distance for functional data as a measure of proximity between functional
observations. The performance of several well known functional classification
procedures are compared with those methods used in conjunction with the
Mahalanobis distance for functional data, with positive results, through a
Monte Carlo study and the analysis of two real data examples.
