Lp norm convergence of rational orthonormal basis function expansions

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Abstract

In this paper model sets for discrete-time LTI systems that are spanned by generalized orthonormal basis functions are investigated. It is established that the partial sums of Fourier series of generalized orthonormal basis expansions converge in all the spaces Lp, and Hp, 1 < p < ∞. It is introduced a rational interpolation operator on nodes given on the unit circle. By using a generalization of the Marcinkiewicz classical Lp norm convergence theorems for triginometric interpolation Lp norm convergence is proved for the discrete rational operators, too.

Original languageEnglish
Pages (from-to)3218-3223
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume4
Publication statusPublished - Dec 1 1999
EventThe 38th IEEE Conference on Decision and Control (CDC) - Phoenix, AZ, USA
Duration: Dec 7 1999Dec 10 1999

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ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

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