Abstract
Every holomorphic function defined on a domain in ℂn is locally representable by a power series and is therefore a local uniform limit of polynomials in n variables. In the case of an arbitrary pair [Σ, a] the analogy with [ℂn, ℘] suggests consideration of functions that are defined on subsets of Σ and are local uniform limits of elements from the algebra G. Such functions turn out to have many nice properties. On the other hand, as might be expected in the general situation, there are complications not present in the case of [ℂn, ℘]. For this reason it will be convenient to begin with a somewhat more general setup involving certain presheaves of continuous functions. At this point the presheaf terminology is used primarily to simplify the discussion.
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© 1979 Springer-Verlag New York Inc.
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Rickart, C.E. (1979). Holomorphic Functions. In: Natural Function Algebras. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8070-2_4
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DOI: https://doi.org/10.1007/978-1-4613-8070-2_4
Publisher Name: Springer, New York, NY
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