On spectral asymptotics of the tensor product of operators with almost regular marginal asymptotics. (English. Russian original) Zbl 1435.47030
St. Petersbg. Math. J. 29, No. 6, 1007-1029 (2018); translation from Algebra Anal. 29, No. 6, 197-229 (2017).
Summary: The spectral asymptotics of a tensor product of compact operators in Hilbert space with known marginal asymptotics is studied. The methods of A. Karol’ et al. [Trans. Am. Math. Soc. 360, No. 3, 1443–1474 (2008; Zbl 1136.60024)] 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.
MSC:
| 47A80 | Tensor products of linear operators |
| 47B02 | Operators on Hilbert spaces (general) |
| 60G15 | Gaussian processes |
Citations:
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