On spectral asymptotics of the tensor product of operators with almost regular marginal asymptotics

摘要

The spectral asymptotics of a tensor product of compact operators in Hilbert space with known marginal asymptotics is studied. The methods of A. Karol', A. Nazarov, and Ya. Nikitin are generalized to operators with almost regular marginal asymptotics. In many (but not all) cases it is shown that the tensor product in question also has almost regular asymptotics. The results are then applied to the theory of small ball probabilities of Gaussian random fields.