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Solvability conditions for some difference operators
Advances in Difference Equations volume 2005, Article number: 514375 (2005)
Infinite-dimensional difference operators are studied. Under the assumption that the coefficients of the operator have limits at infinity, limiting operators and associated polynomials are introduced. Under some specific conditions on the polynomials, the operator is Fredholm and has the zero index. Solvability conditions are obtained and the exponential behavior of solutions of the homogeneous equation at infinity is proved.
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Apreutesei, N.C., Volpert, V.A. Solvability conditions for some difference operators. Adv Differ Equ 2005, 514375 (2005). https://doi.org/10.1155/ADE.2005.1