Hilbert Spaces and Fourier Series

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


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
$$\left( {u,v} \right) = \frac{1}{{2\pi }}\int_0^{2\pi } {u(x)v(x)*dx.}$$


Hilbert Space Fourier Series Orthonormal Basis Fourier Coefficient Cauchy Sequence 
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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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