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  • George Bachman
  • Lawrence Narici
  • Edward Beckenstein
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  • 1.1k Downloads
Part of the Universitext book series (UTX)

Abstract

The classical subject of Fourier series is about approximating periodic functions by sines and cosines, specifically, about expressing an arbitrary periodic function as an infinite series of sines and cosines. (Any function that vanishes outside some interval can be viewed as a periodic function on Rby merely extending it periodically.) The sines and cosines are the “basic” periodic functions in terms of which we express all others. To use — chemical analogy, the sines and cosines are the atoms; the other functions are the molecules. Unlike the physical situation, however, there can be other atoms, other functions, that can serve as the “basic” functions just as effectively as sines and cosines.

Keywords

Hilbert Space Orthonormal Base Orthogonal Projection Product Space Linear Span 
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 New York 2000

Authors and Affiliations

  • George Bachman
    • 1
  • Lawrence Narici
    • 2
  • Edward Beckenstein
    • 3
  1. 1.Emeritus of MathematicsPolytechnic UniversityBrooklynUSA
  2. 2.Department of Mathematics and Computer ScienceSt. John’s UniversityJamaicaUSA
  3. 3.Science DivisionSt. John’s UniversityStaten IslandUSA

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