  A slice regular analogue of the Malmquist-Takenaka system is investigated. It
is proved that they form a complete orthonormal system in the quaternionic
Hardy spaces of the unit ball. The properties of associated projection operator
are studied.
  Key Words and Phrases: Functions of hypercomplex variables, quaternionic
Hardy spaces, series expansions, interpolation, approximation by rational
functions, quaternionic Malmquist-Takenaka system
