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Abstract: We find the logarithmic $L 2$-small ball asymptotics for a class of zero meanGaussian fields with covariances having the structure of -tensor product-. Themain condition imposed on marginal covariances is slow growth at the origin ofcounting functions of their eigenvalues. That is valid for Gaussian functionswith smooth covariances. Another type of marginal functions considered as wellare classical Wiener process, Brownian bridge, Ornstein-Uhlenbeck process,etc., in the case of special self-similar measure of integration. Our resultsare based on new theorem on spectral asymptotics for the tensor products ofcompact self-adjoint operators in Hilbert space which is of independentinterest. Thus, we continue to develop the approach proposed in the paper\cite{KNN}, where the regular behavior at infinity of marginal eigenvalues wasassumed.



Autor: Andrei I. Karol', Alexander I. Nazarov

Fuente: https://arxiv.org/



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