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
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.
|Ministry of Education and Science of the Republic of Kazakhstan
|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.
PDF file (422 kB)
MSC: 39A70, 47B39
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
\paper Discreteness and estimates of spectrum of a first order difference operator
\jour Eurasian Math. J.
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