  Regarding quaternions as normal matrices, we first characterize the $2\times
2$ matrix-valued functions, defined on subsets of quaternions, whose values are
quaternions. Then we investigate the regularity of quaternionic-valued
functions, defined by the analytic functional calculus. Constructions of
analytic functional calculi for real linear operators, in particular for
quaternionic linear ones, are finally discussed, using a Riesz-Dunford-Gelfand
type kernel in one variable, or a Martinelly type kernel in two variables.
