  We study various aspects of Schur analysis in the slice hyperholomorphic
setting. We present two sets of results: first, we give new results on the
functional calculus for slice hyperholomorphic functions. In particular, we
introduce and study some properties of the Riesz projectors. Then we prove a
Beurling-Lax type theorem, the so-called structure theorem. A crucial fact
which allows to prove our results, is the fact that the right spectrum of a
quaternionic linear operator and the S-spectrum coincide. Finally, we study the
Krein-Langer factorization for slice hyperholomorphic generalized Schur
functions. Both the Beurling-Lax type theorem and the Krein-Langer
factorization are far reaching results which have not been proved in the
quaternionic setting using notions of hyperholomorphy other than slice
hyperholomorphy
