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I am looking at a space of holomorphic functions defined on an unbounded set in C. This space contains unbounded functions (but bounded on compact subsets).

What is the classical/typical norm one would use on such a function space?

Thanks

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    It may be worth noting that the space you describe cannot be given any complete, submultiplicative norm, since it contains functions $f$ such that $f(\Omega)$ is unbounded, while all elements of a Banach algebra must have compact spectrum.2012-08-06

2 Answers 2