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Extending bounded type holomorphic mappings on a Banach space. (English) Zbl 1066.46038
Authors’ abstract: We show that a Riemann domain $$\Omega$$ over a symmetrically regular Banach space $$E$$ admits holomorphic extension to pseudo-convex domains over $$E^{..}$$ with respect to two natural spaces of holomorphic functions of bounded type on $$\Omega$$.

##### MSC:
 46G20 Infinite-dimensional holomorphy
Full Text:
##### References:
 [1] Aron, R.; Berner, P., A hahn – banach extension theorem for analytic mappings, Bull. soc. math. France, 106, 3-24, (1978) · Zbl 0378.46043 [2] Aron, R.; Galindo, P.; Garcı́a, D.; Maestre, M., Regularity and algebras of analytic functions in infinite dimensions, Trans. amer. math. soc., 348, 543-559, (1996) · Zbl 0844.46024 [3] Davie, A.M.; Gamelin, T.W., A theorem on polynomial-star approximation, Proc. amer. math. soc., 106, 351-356, (1989) · Zbl 0683.46037 [4] Dineen, S., Complex analysis on infinite dimensional spaces, Monogr. math., (1999), Springer-Verlag London · Zbl 1034.46504 [5] Galindo, P.; Garcı́a, D.; Maestre, M., Entire functions of bounded type on Fréchet spaces, Math. nachr., 161, 185-198, (1993) · Zbl 0797.46037 [6] Köthe, G., Topological vector spaces I, (1969), Springer-Verlag London [7] Mujica, J., Complex analysis in Banach spaces, (1986), North-Holland Amsterdam
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