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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

Holomorphic Function Analytic Continuation Unitary Representation Toeplitz Operator Bergman Space 
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 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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