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Hilbert Spaces and Fourier Series

  • Richard Beals
Part of the Graduate Texts in Mathematics book series (GTM, volume 12)

Abstract

Suppose u and v are in C, the space of continuous complex-valued periodic functions. The inner product of u and v is the number (u,v) defined by
$$\left( {u,v} \right) = \frac{1}{{2\pi }}\int_0^{2\pi } {u(x)v(x)*dx.}$$
(1)

Keywords

Hilbert Space Fourier Series Orthonormal Basis Fourier Coefficient Cauchy Sequence 
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 1973

Authors and Affiliations

  • Richard Beals
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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