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Eurasian Math. J., 2018, Volume 9, Number 2, Pages 89–94 (Mi emj300)  

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.

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan AP05131649/GF5
This work is partially supported by project AP05131649/GF5 of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan and by the L.N. Gumilyov Eurasian National University Research Fund.


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MSC: 39A70, 47B39
Received: 12.06.2017
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Citation: K. N. Ospanov, “Discreteness and estimates of spectrum of a first order difference operator”, Eurasian Math. J., 9:2 (2018), 89–94

Citation in format AMSBIB
\Bibitem{Osp18}
\by K.~N.~Ospanov
\paper Discreteness and estimates of spectrum of a first order difference operator
\jour Eurasian Math. J.
\yr 2018
\vol 9
\issue 2
\pages 89--94
\mathnet{http://mi.mathnet.ru/emj300}


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