Abstract :
Let L denote the operator generated in l 2Ž . by the difference expression
Žl y.n an 1yn 1 bnyn anyn 1, n 0, 1, 2, . . .4, where an4n
and bn4n are complex sequences. In this paper we investigated the spectrum,
the spectral singularities, and the properties of the principal vectors corresponding
to the spectral singularities of L. We also studied similar problems for the discrete
Dirac operator M generated in l 2 Ž , 2 . by the system of difference expression
Ž 1 y.n ynŽ2. pnynŽ1.
Ž y.n y Ž1. Ž2. , n , ž / Ž . ž / 2 n yn 1 qnyn
where
yŽ1.
n y , Ž2. ½ž /5 yn n
is the forward difference operator, i.e., ynŽ i. ynŽ i . 1 ynŽ i., i 1, 2, and
pn4n , qn4n are complex sequences
