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Electronic Journal of Qualitative Theory of Differential Equations 2007, No. 11, 1-29; http://www.math.u-szeged.hu/ejqtde/
 

Summary: Electronic Journal of Qualitative Theory of Differential Equations
2007, No. 11, 1-29; http://www.math.u-szeged.hu/ejqtde/
q-DOMINANT AND q-RECESSIVE MATRIX SOLUTIONS FOR
LINEAR QUANTUM SYSTEMS
DOUGLAS R. ANDERSON AND LISA M. MOATS
Abstract. In this study, linear second-order matrix q-difference equations are
shown to be formally self-adjoint equations with respect to a certain inner prod-
uct and the associated self-adjoint boundary conditions. A generalized Wronskian
is introduced and a Lagrange identity and Abel's formula are established. Two
reduction-of-order theorems are given. The analysis and characterization of q-
dominant and q-recessive 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 second-order linear self-adjoint matrix q-difference system, especially
in the case that admits q-dominant and q-recessive solutions at infinity. Historically,
dominant and recessive solutions of linear matrix differential systems of the form
(PX ) (t) + Q(t)X(t) = 0

  

Source: Anderson, Douglas R. - Department of Mathematics and Computer Science, Concordia College

 

Collections: Mathematics