(1) Department of Mathematics and Statistics, University of Calgary, 2500 University Drive, Calgary, AB, Canada, T2N 1N4;(2) Departamento de Matemáticas, Instituto Venezolano de Investigaciones Cientí ficas, Apartado 20513, Apartado 21827, Caracas, Venezuela, 1020A;(3) Escuela de Matemáticas, Facultad de Ciencias, Universidad Central de Venezuela, Apartado 20513, Caracas, 1020A, Venezuela
Abstract:
We consider a vector-valued Hermite-type basis for which the eigenvalue problem associated to the operator HA,B:=B(;x2)+Ax2 acting on becomes a three-terms recurrence. Here A and B are 2 × 2 constant positive definite matrices. Our main result provides an explicit characterization of the eigenvectors of HA,B that lie in the span of the first four elements of this basis when ABBA.This revised version was published online in March 2005 with corrections to the cover date.
;x2)+Ax2 acting on
becomes a three-terms recurrence. Here A and B are 2 × 2 constant positive definite matrices. Our main result provides an explicit characterization of the eigenvectors of HA,B that lie in the span of the first four elements of this basis when AB 
BA.This revised version was published online in March 2005 with corrections to the cover date.