The aim of this paper is the following: Firstly give the explicit constructions of the infinitesimal deformation of Coh(X). Here X is a smooth projective variety. Secondly we show the Fourier-Mukai transform Φ: D(X) → D(Y ) extends to an equivalence between the derived categories of the deformed categories.

We consider the asymptotic behavior of Fourier transforms of stationary and ergodic sequences. Under sufficiently mild conditions, central limit theorems are established for almost all frequencies as well as for a given frequency. Applications to the widely used linear processes and iterated random functions are discussed. Our results shed new light on the foundation of spectral analysis in tha...