[Author] A. I. Nazarov [Title] Exact $L_2$-small ball asymptotics of Gaussian processes and the spectrum of boundary value problems with "non-separated" boundary conditions [AMS Subj-class] 60G15 Gaussian processes 34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions [Keywords] Gaussian processes, small ball asymptotics, spectral asymptotics [Abstract] We sharpen a classical result on the spectral asymptotics of the 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, integrated generalized Slepian process, integrated centered Wiener process and integrated centered Brownian bridge. [Comments] Russian, 25 pp. [Contact e-mail] an@AN4751.spb.edu