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Mathematics > Spectral Theory

arXiv:1804.00187 (math)
[Submitted on 31 Mar 2018]

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

Authors:N. V. Rastegaev
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Abstract: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.
Subjects: Spectral Theory (math.SP)
Cite as: arXiv:1804.00187 [math.SP]
  (or arXiv:1804.00187v1 [math.SP] for this version)
  https://doi.org/10.48550/arXiv.1804.00187

Submission history

From: Nikita Rastegaev [view email]
[v1] Sat, 31 Mar 2018 16:00:10 UTC (21 KB)
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