Function Spaces

  • Adam Korányi
Chapter
Part of the Progress in Mathematics book series (PM, volume 185)

Abstract

The interest of the Hilbert spaces L λ 2 , of Chapter V is due to the fact that the group G of holomorphic automorphisms of D acts on them by (irreducible) unitary representations. This statement must be made a little more precise. A unitary (resp. bounded) representation is properly speaking a strongly continuous homomorphism gT (g)into the unitary (resp. bounded) transformations of a Hilbert space, such that T (g) T (h) = T (gh) for all g,h∈G. A slightly more general notion is that of a (unitary, or bounded) projective representation,where one requires only T (g)T (h) = c (g, h)T (gh) with some c (g, h) ∈ ℂ.

Keywords

Wallach Bonami 

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Adam Korányi
    • 1
  1. 1.Dept. Mathematics & Computer ScienceH.H. Lehman CollegeBronxUSA

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