Group Representations and Unbounded Operators
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.
KeywordsHilbert Space Compact Group Unitary Representation Unitary Transformation Selfadjoint Operator
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