On the Characterization of a Class of Difference Equations
نویسندگان
چکیده
We focus on the behavior of solutions of the difference equation xn b1xn−1 b2xn−2 · · · bnx0 yn, n 1, 2, . . ., where bk is a fixed sequence of complex numbers, and yk is a fixed sequence in a complex Banach space. We give the general solution of this difference equation. To examine the asymptotic behavior of solutions, we compute the spectra of operators which correspond to such type of difference equations. These operators are represented by upper triangular or lower triangular infinite banded Toeplitz matrices.
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