Spectral Representation of Unitary Operators

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


The main topic of this chapter is the spectral representation of unitary operators as well as one-parameter groups of unitary operators. That is, the problem is how to represent such objects by certain analogues of Fourier transforms. We are going to describe theories based upon the Herglotz–Bochner theorem already discussed in Chap.  6. However, the Herglotz–Bochner theorem can be conversely deduced from the spectral representation theorem of unitary operators.


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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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