Modified Prony Algorithm for an Inhomogeneous Linear Ordinary Differential Equation with Constant Coefficients

摘要

The analytic continuation of functions defined on a bounded (or discrete) set is a popular problem in complex analysis (see, e.g., [1–3]). A special case is the reconstruction of a quasi-polynomial from its values at a finite number of uniform grid points, which is a problem going back to Prony. Various modifications of the Prony algorithm were overviewed in [4, Ch. 11; 5,Ch. 2]. This paper deals with an inverse problem for an inhomogeneous linear ordinary differential equation (LODE) with constant coefficients (version of Prony’s method). An engineering version of this modification was considered in [6].