Solvability conditions for some difference operators
V. A. Volpert, N. C. Apreutesei
Advances in Difference Equations · 2005
doi:10.1155/ade.2005.1 (opens in a new tab)
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Abstract
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.
Abstract licence: CC BY
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