Fourier Transforms of Measures

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


So far, we have studied Fourier transforms or Fourier coefficients of functions defined on \(\mathbb {R}\) or \(\mathbb {T}\). Inverse procedures to recover original functions from given Fourier transforms or Fourier coefficients were also discussed (spectral synthesis). However, there are many functions to which the methods of classical Fourier analysis can not be applied. In this chapter, we develop the theory of Fourier transforms of measures as a similar but new method to overcome such difficulties.


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

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

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