Exact L 2-Small Ball Asymptotics of Gaussian Processes and the Spectrum of Boundary-Value Problems

We sharpen a classical result on the spectral asymptotics of boundary-value problems for self-adjoint ordinary differential operator. Using this result, we obtain the exact L (2)-small ball asymptotics for a new class of zero-mean Gaussian processes. This class includes, in particular, the integrated generalized Slepian process, integrated centered Wiener process, and integrated centered Brownian bridge.