The spectral estimation problem in infinite-dimensional spaces
type: Item
instance of: scholarly article
title: The spectral estimation problem in infinite-dimensional spaces
zbMATH Open document ID: 1348.46074
published in: Journal of Mathematical Sciences (New York)
publication date: 2016-05-10T00:00:00Z
review text: 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.
reviewed by: David Seifert
Mathematics Subject Classification ID: 46N20
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 6578572
zbMATH Keywords: spectral estimation problem
zbMATH Keywords: boundary control
zbMATH Keywords: inverse theory
author: Sergei Avdonin
author: Victor Mikhaylov
MaRDI profile type: Publication
full work available at URL: s10958-015-2307-7
OpenAlex ID: W2056706225
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DOI: 10.1007/S10958-015-2307-7
description: scientific article; zbMATH DE number 6578572