A Spectral Theory for Nonautonomous Difference Equations

For nonautonomoua linear difference equati01111 z•+t = A•z• with invertible matrix coefficient• A• E B.N xN, k E Z, the 10-called dichotomy 11pectrum ia introduced in thi1 paper. Thia new 1pectrum couilt1 of at most N clOied in-

Consider a linear system of difference equations

(1)

with invertible matrix coefficients At E aN)(N. Let ~ : z X z - aNxN I (k, t) ~--+ ~(k, t) denote its evolution operator, i.e.,

{

of projections P~:, k E Z, such that