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This article is cited in 14 scientific papers (total in 14 papers)
Difference operators and operator-valued matrices of the second order
A. G. Baskakov, A. Yu. Duplishcheva Voronezh State University
Abstract:
We study linear difference operators
(equations) of the second order. We give
conditions under which they are invertible
or Fredholm and obtain asymptotic
representations for solutions of homogeneous
difference equations. Our main results are
obtained by assigning an operator-valued
matrix of the second order to the given
operator and then using the theory
of difference operators of the first order
determined by these matrices.
Keywords:
linear difference operator, invertible operator, spectrum of an operator, exponential
dichotomy, invertibility state of a linear operator, asymptotic behaviour of solutions.
Received: 29.04.2014
Citation:
A. G. Baskakov, A. Yu. Duplishcheva, “Difference operators and operator-valued matrices of the second order”, Izv. RAN. Ser. Mat., 79:2 (2015), 3–20; Izv. Math., 79:2 (2015), 217–232
Linking options:
https://www.mathnet.ru/eng/im8248https://doi.org/10.1070/IM2015v079n02ABEH002740 https://www.mathnet.ru/eng/im/v79/i2/p3
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Abstract page: | 1882 | Russian version PDF: | 496 | English version PDF: | 14 | References: | 122 | First page: | 106 |
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