Abstract
One of the general methods in linear control theory is based on harmonic and non-harmonic Fourier series. The key of this approach is the establishment of various suitable adaptations and generalizations of the classical Parseval equality. A new and systematic approach was begun in our papers [1]-[4] in collaboration with Baiocchi. Many recent results of this kind, obtained through various Ingham-type theorems, were exposed recently in [9]. Although this work concentrated on continuous models, in connection with numerical simulations a natural question is whether these results also admit useful discrete versions. The purpose of this paper is to establish discrete versions of various Ingham-type theorems by using our approach. They imply the earlier continuous results by a simple limit process.
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Komornik, V., Loreti, P. Semi-Discrete Ingham-Type Inequalities. Appl Math Optim 55, 203–218 (2007). https://doi.org/10.1007/s00245-006-0888-8
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DOI: https://doi.org/10.1007/s00245-006-0888-8