Entire vectors and holomorphic extension of representations. II
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- by Richard Penney PDF
- Trans. Amer. Math. Soc. 191 (1974), 195-207 Request permission
Abstract:
Let G be a connected, simply connected Lie group and let ${G_c}$ be its complexification. Let U be a unitary representation of G. The space of vectors v at which U is holomorphically extendible to ${G_c}$ is denoted $\mathcal {H}_\infty ^\omega (U)$. In [9] we characterized those U for which $\mathcal {H}_\infty ^\omega$ is dense. In the present work we study $\mathcal {H}_\infty ^\omega$ as a topological vector space, proving e.g., that $\mathcal {H}_\infty ^\omega$ is a Montel space if U is irreducible and G is nilpotent. We prove a representation theorem for $(\mathcal {H}_\infty ^\omega )’$ 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.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 191 (1974), 195-207
- MSC: Primary 22E45
- DOI: https://doi.org/10.1090/S0002-9947-1974-0364556-9
- MathSciNet review: 0364556