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Exact treatment of operator difference equations with nonconstant noncommutative coefficients

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Type
Preprint
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Submission Date
Identifiers
arXiv ID: 1206.5899
Source
arXiv
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Abstract

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.

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