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Fourier Series on Hilbert Spaces

  • Toru Maruyama
Chapter
Part of the Monographs in Mathematical Economics book series (MOME, volume 2)

Abstract

Let e1, e2, …, el be the standard basis of an l-dimensional Euclidean space consisting of l unit vectors. Then any vector x can be expressed as
$$\displaystyle x=\sum _{i=1}^l c_ie_i $$
and such an expression is determined uniquely. The coefficients c1, c2, ⋯, cl are computed as ci = 〈x, ei〉 (inner product).

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Toru Maruyama
    • 1
  1. 1.Professor EmeritusKeio UniversityTokyoJapan

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