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Applications to Analysis

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

Abstract

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))
$$ {\omega^n}(\rlap{--}{k})v({\beta_1},...,{\beta_n}) = \sum\limits_{{j = 1}}^n {({\beta_j} + \frac{1}{2})} v({\beta_1},...,{\beta_n}) $$
(1.1.1)
.

Keywords

Invariant Measure Fundamental Solution Light Cone Invariant Distribution High Weight Vector 
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 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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