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Numerical Aspects of Time and Band Limiting

  • Jeffrey A. Hogan
  • Joseph D. Lakey
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

This chapter is concerned with the role of the prolates in numerical analysis— particularly their approximation properties and application in the numerical solution of differential equations. The utility of the prolates in these contexts is due principally to the fact that they form a Markov system (see Defn. 2.1.6) of functions on [11], a property that stems from their status as eigenfunctions of the differential operator \( {\mathcal P} \) of (1.6), and allows the full force of the Sturm–Liouville theory to be applied. The Markov property immediately gives the orthogonality of the prolates on [11] (previously observed in Sect. 1.2 as the double orthogonality property) and also a remarkable collection of results regarding the zeros of the prolates as well as quadrature properties that are central to applications in numerical analysis.

Keywords

Spectral Element Numerical Aspect Spectral Element Method Band Limit Markov System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.School of Mathematical and Physical SciencesUniversity of NewcastleCallaghanAustralia
  2. 2.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA

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