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Eurasian Mathematical Journal, 2018, Volume 9, Number 2, Pages 89–94
(Mi emj300)
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This article is cited in 2 scientific papers (total in 2 papers)
Short communications
Discreteness and estimates of spectrum of a first order difference operator
K. N. Ospanov Department of Mechanics and Mathematics,
L.N. Gumilyov Eurasian National University,
13 Munaitpasov St,
010008 Astana, Kazakhstan
Abstract:
We investigated a minimal closed in the space $l_2$ first order nonsymmetric difference operator $L$. The matrix of zero order coefficients of $L$ may be an unbounded operator. The study of $L$ is motivated by applications to stochastic processes and stochastic differential equations. We obtained compactness conditions and exact with respect to the order two-sided estimates for $s$-numbers of the resolvent of $L$. Note that these estimates for $s$-numbers do not depend on the oscillations of the coefficients of $L$, in contrast to the case of a differential operator.
Keywords and phrases:
difference operator, coercive estimate, compactness of the resolvent, singular numbers.
Received: 12.06.2017
Citation:
K. N. Ospanov, “Discreteness and estimates of spectrum of a first order difference operator”, Eurasian Math. J., 9:2 (2018), 89–94
Linking options:
https://www.mathnet.ru/eng/emj300 https://www.mathnet.ru/eng/emj/v9/i2/p89
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Abstract page: | 186 | Full-text PDF : | 85 | References: | 23 |
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