The spectral estimation problem in infinite-dimensional spaces
Consider a signal \[ s(t)=\sum_{k=1}^Na_ke^{\lambda_kt},\quad t\geq0, \] where \(N\in\mathbb N\) and \(a_k,\lambda_k\), \(1\leq k\leq N\), are complex numbers. The classical \textit{spectral estimation problem} consists of recovering the coefficients \(a_k,\lambda_k\), \(1\leq k\leq N\), of the signal \(s\) from given observations \(s(j)\), \(0\leq j\leq N-1\). The authors consider an infinite-dimensional version of this problem and solve it using a boundary control approach. The paper concludes with an application to the initial value problem for a hyperbolic system.
scientific article; zbMATH DE number 6578572