Entire vectors and holomorphic extension of representations. II

Author:
Richard Penney

Journal:
Trans. Amer. Math. Soc. **191** (1974), 195-207

MSC:
Primary 22E45

Part I:
Trans. Amer. Math. Soc. **198** (1974), 107-121

MathSciNet review:
0364556

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Abstract: Let *G* be a connected, simply connected Lie group and let be its complexification. Let *U* be a unitary representation of *G*. The space of vectors *v* at which *U* is holomorphically extendible to is denoted . In [9] we characterized those *U* for which is dense. In the present work we study as a topological vector space, proving e.g., that is a Montel space if *U* is irreducible and *G* is nilpotent. We prove a representation theorem for which yields a Bergman kernel type theorem for *G*. As an application we give a necessary and sufficient condition for the set of holomorphic functions on certain solvmanifolds to separate points.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0364556-9

Keywords:
Analytic vector,
Lie group,
solvmanifold

Article copyright:
© Copyright 1974
American Mathematical Society