The Spectral Theorem

  • William F. DonoghueJr.
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 207)


The study of Pick functions has long been associated with certain problems in analysis, in particular the Moment Problem and the theory of the spectral representation of self-adjoint operators in Hilbert space. The traditional proof of the spectral theorem deduces it from the integral representation of Pick functions given in Chapter II, and this argument has the advantage that the self-adjoint operator under study need not be supposed continuous. This chapter is devoted to that proof.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • William F. DonoghueJr.
    • 1
  1. 1.University of CaliforniaIrvineUSA

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