Exact treatment of operator difference equations with nonconstant   noncommutative coefficients
  In this paper we study in a Hilbert space a homogeneous linear second order difference equation with nonconstant and noncommuting operator coefficients. We build its exact resolutive formula consisting in the explicit non-iterative expression of a generic term of the unknown sequence of vectors of the Hilbert space. Some non-trivial applications are reported with the aim of showing the usefulness and the broad applicability of our result. 
M. A. Jivulescu, A. Messina
math-ph math.MP