The Generalized Operator Based Prony Method

by Kilian Stampfer
Doctoral thesis
Date of Examination:2019-01-17
Date of issue:2019-05-10
Advisor:Prof. Dr. Gerlind Plonka-Hoch
Referee:Prof. Dr. Gerlind Plonka-Hoch
Referee:Prof. Dr. Stefan Kunis
Persistent Address: http://dx.doi.org/10.53846/goediss-7406

 

 

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Abstract

English

The well known Prony method was introduced to reconstruct finite linear combinations of complex exponentials. A first approach towards generalizing this method to more arbitrary expansions was made by Peter & Plonka in 2013. Based on their work, this thesis generalizes the classical Prony method in a purely operator-based way to finite linear combinations of eigenfunctions of certain linear operators. The major achievements are thereby a more flexible way of data acquisition and a full embedding of all existing examples of the classical Prony method. Furthermore, new examples including the Stieltjes-Wigert polynomials have been given and it was also possible to derive a general treatment of linear combinations into Sturm-Liouville type polynomials in the context of the Prony method.
Keywords: generalized Prony method; exponential operators; sparse expansions into eigenfunctions of linear operators; parameter identification; generalized sampling
 
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