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- W2068045224 abstract "Let E be a separable Banach spaceU be a non-empty open subset of E τ be a strictly lower semicontinuous function on U such that d(x, ∂U) ≥ τ(x) for x ∊ U. Let Bτ (U) denote the collection of all finite unions of closed balls [Bbar] p (x) with center x ∊ U and ρ < τ (x); and, let Hτ(U) be the algeba of the complex holomorphic functions in U which are hounded in every set of Bτ(U) furnished with the Frechet topology of the uniform convergence over the elements of Bτ(U). The main results of this paper are: if A ∊ Bτ(U), then A is bounded, if and onlu, if, its τ-holomorphy hull is bounded; if A ∊ Bτ(U) and and zo is an element of the τ-holomorphy hull of A, then every f ∊ Hτ(U) is holomorphic on Br (zo) and for every , where ; if U is bounded the following are equivalent: (i) U is a domain of τ-holomorphy. (ii) U is τ-holomorphically convex. (iii) Every boundary point of U is τ-esential. (iv) For every sequence in U with then there exists a mapping f ∊ Hτ(U) such that ." @default.
- W2068045224 created "2016-06-24" @default.
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- W2068045224 date "1994-01-01" @default.
- W2068045224 modified "2023-09-25" @default.
- W2068045224 title "Domains of τ-holomorphy in a complex separable banach space" @default.
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- W2068045224 doi "https://doi.org/10.1080/17476939408814701" @default.
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