부산대학교 도서관

Authors' summary: ``Let $Y$ be a family of sequences defined by lineardifference equations of the form $y(n+1)=P(n)y(n)+Q(n)$, where $P$ and $Q$are restricted to be polynomials of limited degree, constant matrices,multinomials, and so forth. The central problem is to find a finite samplewhich uniquely identifies members of $Y$. It is shown that such a sampleexists when $P$ and $Q$ are polynomials of limited degree. The sample sizedepends linearly on the degree limits. A similar result holds for systemsof difference equations with $P$ a constant matrix and $Q$ a column vectorwith polynomial components. Testingprocedures are also derived for the case where the coefficients of $P$ and$Q$ are multinomials in a vector parameter $x$, and $y$ is considered to bea function of its initial value.''