Difference equations of second order with spectral singularities ✩

In this paper using the uniqueness theorem of analytic functions we investigated the eigenvalues and the spectral singularities of the difference equation an−1yn−1 + bnyn + anyn+1 = λyn, n∈ Z = {0,±1,±2, . . .}, where t {an}n∈Z, {bn}n∈Z are complex sequences and λ is a spectral parameter.  2003 Elsevier Science (USA). All rights reserved.