Sharp Small Deviation Asymptotics in the L 2-Norm for a Class of Gaussian Processes

We characterize the exact behavior of small deviations in a Hilbert norm for centered Gaussian processes in the case where their covariances have a special form of eigenvalues. This result enables us to describe small deviation asymptotics for certain Gaussian processes. Bibliography: 20 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 214–221.