This article is cited in 6 papers

Spectral Asymptotics for Problems with Integral Constraints

Yu. P. Petrova

Saint Petersburg State University

Abstract: The eigenvalue problem for differential operators of arbitrary order with integral constraints is considered. The asymptotics of the eigenvalues is obtained. The results are applied to finding the asymptotics of the probability of small deviations for some detrended processes of $n$th order.

Keywords: spectral asymptotics, Gaussian process, small deviation.

UDC: 517

Received: 13.08.2016

DOI: 10.4213/mzm11344

 English version: Mathematical Notes, 2017, 102:3, 369–377

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