1206.5899 (M. A. Jivulescu et al.)

Exact treatment of operator difference equations with nonconstant
noncommutative coefficients    [PDF]

M. A. Jivulescu, A. Messina

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.

View original: http://arxiv.org/abs/1206.5899