Plancherel Theorem Website Links For
Theorem
 

Information About

Plancherel Theorem




Here Plancherel's version concerns spaces of functions on the Real Line . The theorem is valid in abstract versions, on Locally Compact Abelian Group s in general. Even more generally, there is a version of the Plancherel theorem which makes sense for non-commutative locally compact groups satisfying certain technical assumptions. This is the subject of Non-commutative Harmonic Analysis .

The unitarity of the Fourier transform is often called Parseval's Theorem in science and engineering fields, based on an earlier (but less general) result that was used to prove the unitarity of the Fourier Series .


REFERENCES


  • J. Dixmier, ''Les C
    algèbres et leurs Represéntations'', Gauthier Villars, 1969

  • K. Yosida, ''Functional Analysis'', Springer Verlag, 1968