  In this paper we develop the spectral theory of the fractional Brownian
motion (fBm) using the ideas of Krein's work on continuous analogous of
orthogonal polynomials on the unit circle. We exhibit the functions which are
orthogonal with respect to the spectral measure of the fBm and obtain an
explicit reproducing kernel in the frequency domain. We use these results to
derive an extension of the classical Paley-Wiener expansion of the ordinary
Brownian motion to the fractional case.
