 
Summary: Electronic Journal of Qualitative Theory of Differential Equations
2007, No. 11, 129; http://www.math.uszeged.hu/ejqtde/
qDOMINANT AND qRECESSIVE MATRIX SOLUTIONS FOR
LINEAR QUANTUM SYSTEMS
DOUGLAS R. ANDERSON AND LISA M. MOATS
Abstract. In this study, linear secondorder matrix qdifference equations are
shown to be formally selfadjoint equations with respect to a certain inner prod
uct and the associated selfadjoint boundary conditions. A generalized Wronskian
is introduced and a Lagrange identity and Abel's formula are established. Two
reductionoforder theorems are given. The analysis and characterization of q
dominant and qrecessive solutions at infinity are presented, emphasizing the case
when the quantum system is disconjugate.
1. Introduction
Quantum calculus has been utilized since at least the time of Pierre de Fermat
[10, Chapter B.5] to augment mathematical understanding gained from the more
traditional continuous calculus and other branches of the discipline [3]. In this study
we will analyze a secondorder linear selfadjoint matrix qdifference system, especially
in the case that admits qdominant and qrecessive solutions at infinity. Historically,
dominant and recessive solutions of linear matrix differential systems of the form
(PX ) (t) + Q(t)X(t) = 0
