부산대학교 도서관

Authors' summary: ``Let $Y$ be a family of sequences defined by linear difference 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 sample which uniquely identifies members of $Y$. It is shown that such a sample exists when $P$ and $Q$ are polynomials of limited degree. The sample size depends linearly on the degree limits. A similar result holds for systems of difference equations with $P$ a constant matrix and $Q$ a column vector with polynomial components. Testing procedures 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 be a function of its initial value.''