Applications to Analysis

  • Roger Howe
  • Eng Chye Tan
Part of the Universitext book series (UTX)


We have seen that the Hermite functions on ℝ n , {v(β1,...,βn) | (β1,..., β n ) ∈ ℤ + n } form a k̄ eigenbasis in S(ℝ n ) with (see Chap. III, Eq. (2.1.20))
$$ {\omega^n}(\rlap{--}{k})v({\beta_1},...,{\beta_n}) = \sum\limits_{{j = 1}}^n {({\beta_j} + \frac{1}{2})} v({\beta_1},...,{\beta_n}) $$


Invariant Measure Fundamental Solution Light Cone Invariant Distribution High Weight Vector 
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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Roger Howe
    • 1
  • Eng Chye Tan
    • 2
  1. 1.Department of MathematicsYale UniversityNew HavenUSA
  2. 2.Department of MathematicsNational University of SingaporeSingapore

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