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manuscripta mathematica

, Volume 94, Issue 1, pp 133–149 | Cite as

A unified approach to concrete plancherel theory of homoogeneous spaces

  • Ronald L. Lipsman
Article

Summary

A new paradigm for concrete Plancherel analysis on homogeneous spaces is established wherein the distinction between finite and infinite multiplicity is de-emphasized. A unified treatment — incorporating the Penney-Fujiwara formulation for finite multiplicity and the Bonnet formulation for infinite multiplicity — is presented. The heretofore unrecognized similarities in the two theories are uncovered and emphasized. The unified theory is illustrated with explicit computations of the Plancherel formula for a certain class of homogeneous spaces of semidirect product groups.

Keywords

Invariant Measure Homogeneous Space Haar Measure Multiplicity Function Nuclear Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Ronald L. Lipsman
    • 1
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA

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