Geodesic
Difference operators and operator-valued matrices of the second order
Izvestiya. Mathematics , Tome 79 (2015) no. 2, pp. 217-232

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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. 
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     author = {A. G. Baskakov and A. Yu. Duplishcheva},
     title = {Difference operators and operator-valued matrices of the second order},
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A. G. Baskakov; A. Yu. Duplishcheva. Difference operators and operator-valued matrices of the second order. Izvestiya. Mathematics , Tome 79 (2015) no. 2, pp. 217-232. http://geodesic.mathdoc.fr/item/IM2_2015_79_2_a0/