[Authors]
 Rastegaev, N. V.

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

[AMS Subj-class]
 47A80 Tensor products of operators
 47A75 Eigenvalue problems
 60G15 Gaussian processes
       
[Keywords]
 spectral asymptotics, tensor products of operators, small ball probabilities

[Abstract]
 Spectral asymptotics of a tensor product of compact operators in Hilbert space
 with known marginal asymptotics is studied. Method of A. Karol', A. Nazarov
 and Ya. Nikitin (Trans. AMS, 2008) is 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.

[Comments]
 LaTeX, Russian, 29 pp.

[Contact e-mail]
 rastmusician@gmail.com