Exact treatment of operator difference equations with nonconstant noncommutative coefficients

2012/06/26 by Maria Anastasia Jivulescu, M. A. Jivulescu, A. Messina +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1206.5899

accepted for publication in Journal of Engineering Mathematics

openalex publication_date 2012/06/26 · arxiv created 2012/12/11 · arxiv updated 2012/12/12 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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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