  Spectral asymptotics of a tensor product of compact operators in Hilbert
space with known marginal asymptotics is studied. Methods of A. Karol', A.
Nazarov and Ya. Nikitin (Trans. AMS, 2008) are generalized for operators with
almost regular marginal asymptotics. In many (but not all) cases it is shown,
that tensor product has almost regular asymptotics as well. Obtained results
are then applied to the theory of small ball probabilities of Gaussian random
fields.
