Holomorphic functions on nuclear spaces
Copyright policy )Holomorphic functions on nuclear spaces
The space H ( E ) \mathcal {H}(E) of holomorphic functions on a quasi-complete nuclear space is investigated. If H ( E ) \mathcal {H}(E) is endowed with the compact open topology, it is shown that H ( E ) \mathcal {H}(E) is nuclear if and only if E ′ E’ (continuous dual of E E ) is nuclear. If E E is a D F N \mathcal {D}FN (dual of a Fréchet nuclear space) and F F is a closed subspace of E E , then the restriction mapping H ( E ) → H ( F ) \mathcal {H}(E) \to \mathcal {H}(F) is a surjective strict morphism.
- University College Dublin Ireland
- Le Moyne College United States
Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.), Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces), Topological linear spaces of continuous, differentiable or analytic functions, Other generalizations of function theory of one complex variable
Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.), Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces), Topological linear spaces of continuous, differentiable or analytic functions, Other generalizations of function theory of one complex variable
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