Abstract:
Let H\G be a causal symmetric space sitting inside its complexification H ℂ\G ℂ. Then there exist certain G-invariant Stein subdomains Ξ of H ℂ\G ℂ. The Haar measure on H ℂ\G ℂ gives rise to a G-invariant measure on Ξ. With respect to this measure one can define the Bergman space B 2(Ξ) of square integrable holomorphic functions on Ξ. The group G acts unitarily on the Hilbert space B 2(Ξ) by left translations in the arguments. The main result of this paper is the Plancherel Theorem for B 2(Ξ), i.e., the disintegration formula for the left regular representation into irreducibles.
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Received: Received: 23 November 1998
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Hilgert, J., Krötz, B. Weighted Bergman spaces¶associated with causal symmetric spaces. manuscripta math. 99, 151–180 (1999). https://doi.org/10.1007/s002290050167
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DOI: https://doi.org/10.1007/s002290050167