The Invariant Laplacian

  • Walter Rudin
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 241)

Abstract

Suppose Ω is an open subset of B, fC 2 (Ω), and a ∈ Ω. We define
$$\left( {\tilde \Delta f} \right)\left( a \right) = \Delta \left( {f \circ {\varphi _a}} \right)\left( 0 \right),$$
(1)
where ϕa is the involution defined in §2.2.1, and Δ is the ordinary Laplacian given by
$$\Delta g = 4\sum\limits_{i = 1}^n {{D_i}{{\bar D}_i}g} $$
(2)
as in §1.3.4.

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Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • Walter Rudin
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA

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