Group Representations and Unbounded Operators

  • Irving E. Segal
  • Ray A. Kunze
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 228)


Among a number of important developments emerging from the foregoing discussions none is more logical and significant than the extension of spectral theory to unbounded operators, and related developments in group-representation theory. The theorem of Stone, giving the structure of the general one-parameter continuous unitary group on a Hilbert space, connects with both these matters and is intrinsically important. Its analogs for groups which are either compact or locally compact Abelian are central for harmonic analysis on these groups.


Hilbert Space Compact Group Unitary Representation Unitary Transformation Selfadjoint Operator 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Irving E. Segal
    • 1
  • Ray A. Kunze
    • 2
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.University of California at IrvineIrvineUSA

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